Daily Papers

Automated agent design improves agent harnesses through iterative revision, evaluation, and feedback summarization. Existing methods are largely candidate-centric: cross-round experience is organized around candidate agents, which leaves the repair progress implicit. This causes inefficient repair targeting, slow consolidation of partial progress, and propagation of ineffective interventions across rounds. Therefore, we formulate issue-centric agent optimization, in which repair progress is carried forward as an explicit persistent issue state to guide optimization, rather than re-derived from candidate history in each round. We instantiate the formulation in ADIAS, a framework for automated full-code agent design with two mechanisms. A persistent issue state maintains stable issue identities, lifecycle status, supporting evidence, and intervention-outcome histories. Issue-guided optimization uses this state to jointly propose repair targets and revision directions for subsequent focused full-code modification. Across five interactive benchmarks, ADIAS outperforms the strongest baseline by 25.2% on average and achieves consistent gains across four backbone models. Controlled ablations further show that removing persistent issue state or replacing issue-centric revision with candidate-centric policies leads to performance drops of up to 40.7%.

Recent advances in image-to-video (I2V) generation have achieved remarkable progress in synthesizing high-quality, temporally coherent videos from static images. Among all the applications of I2V, human-centric video generation includes a large portion. However, existing I2V models encounter difficulties in maintaining identity consistency between the input human image and the generated video, especially when the person in the video exhibits significant expression changes and movements. This issue becomes critical when the human face occupies merely a small fraction of the image. Since humans are highly sensitive to identity variations, this poses a critical yet under-explored challenge in I2V generation. In this paper, we propose Identity-Preserving Reward-guided Optimization (IPRO), a novel video diffusion framework based on reinforcement learning to enhance identity preservation. Instead of introducing auxiliary modules or altering model architectures, our approach introduces a direct and effective tuning algorithm that optimizes diffusion models using a face identity scorer. To improve performance and accelerate convergence, our method backpropagates the reward signal through the last steps of the sampling chain, enabling richer gradient feedback. We also propose a novel facial scoring mechanism that treats faces in ground-truth videos as facial feature pools, providing multi-angle facial information to enhance generalization. A KL-divergence regularization is further incorporated to stabilize training and prevent overfitting to the reward signal. Extensive experiments on Wan 2.2 I2V model and our in-house I2V model demonstrate the effectiveness of our method. Our project and code are available at https://ipro-alimama.github.io/.

Current LLM unlearning methods face a critical security vulnerability that undermines their fundamental purpose: while they appear to successfully remove sensitive or harmful knowledge, this ``forgotten" information remains precariously recoverable through relearning attacks. We identify that the root cause is that conventional methods optimizing the forgetting loss at individual data points will drive model parameters toward sharp minima in the loss landscape. In these unstable regions, even minimal parameter perturbations can drastically alter the model's behaviors. Consequently, relearning attacks exploit this vulnerability by using just a few fine-tuning samples to navigate the steep gradients surrounding these unstable regions, thereby rapidly recovering knowledge that was supposedly erased. This exposes a critical robustness gap between apparent unlearning and actual knowledge removal. To address this issue, we propose StableUN, a bi-level feedback-guided optimization framework that explicitly seeks more stable parameter regions via neighborhood-aware optimization. It integrates forgetting feedback, which uses adversarial perturbations to probe parameter neighborhoods, with remembering feedback to preserve model utility, aligning the two objectives through gradient projection. Experiments on WMDP and MUSE benchmarks demonstrate that our method is significantly more robust against both relearning and jailbreaking attacks while maintaining competitive utility performance.

On-policy reinforcement learning has become a central paradigm for improving the reasoning abilities of large language models. However, its effectiveness is often limited by reward sparsity: when a model fails to discover correct trajectories for difficult problems, the optimization process receives little useful signal and may stagnate. Existing approaches mitigate this issue by incorporating off-policy demonstrations, expert traces, or model-generated solutions, but they typically require the auxiliary data to match the format of the reinforcement-learning task, often relying on rejection sampling from stronger models to obtain suitable training trajectories. We introduce Rationale-Guided Policy Optimization (RGPO), a framework that adaptively leverages ground-truth rationale information according to the model's current capability while preserving its freedom to explore. Rather than treating reference solutions as fixed imitation targets, RGPO uses them as temporary scaffolds: rationales help the model generate improved responses, after which only higher-reward, model-generated solutions are transferred back to the original unguided setting. This design allows training to exploit available ground-truth information without requiring off-policy data to follow the same format as the RL task. Across both language-only and vision-language reasoning settings, RGPO consistently improves performance over RLVR baselines, and ablation studies show that adaptive rationale guidance is a key contributor to these gains. These results suggest that RGPO offers a practical and general approach for reducing reward sparsity, stabilizing reinforcement learning, and improving reasoning performance in both text-only and multimodal models.

This study focuses on the topic of offline preference-based reinforcement learning (PbRL), a variant of conventional reinforcement learning that dispenses with the need for online interaction or specification of reward functions. Instead, the agent is provided with fixed offline trajectories and human preferences between pairs of trajectories to extract the dynamics and task information, respectively. Since the dynamics and task information are orthogonal, a naive approach would involve using preference-based reward learning followed by an off-the-shelf offline RL algorithm. However, this requires the separate learning of a scalar reward function, which is assumed to be an information bottleneck of the learning process. To address this issue, we propose the offline preference-guided policy optimization (OPPO) paradigm, which models offline trajectories and preferences in a one-step process, eliminating the need for separately learning a reward function. OPPO achieves this by introducing an offline hindsight information matching objective for optimizing a contextual policy and a preference modeling objective for finding the optimal context. OPPO further integrates a well-performing decision policy by optimizing the two objectives iteratively. Our empirical results demonstrate that OPPO effectively models offline preferences and outperforms prior competing baselines, including offline RL algorithms performed over either true or pseudo reward function specifications. Our code is available on the project website: https://sites.google.com/view/oppo-icml-2023 .

Large Language Models (LLMs) have achieved remarkable success in natural language processing, but their full fine-tuning remains resource-intensive. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have emerged as a practical solution by approximating parameter updates with low-rank matrices. However, LoRA often exhibits a "double descent" phenomenon during fine-tuning, where model performance degrades due to overfitting and limited expressiveness caused by low-rank constraints. To address this issue, we propose LoRA-GGPO (Gradient-Guided Perturbation Optimization), a novel method that leverages gradient and weight norms to generate targeted perturbations. By optimizing the sharpness of the loss landscape, LoRA-GGPO guides the model toward flatter minima, mitigating the double descent problem and improving generalization. Extensive experiments on natural language understanding (NLU) and generation (NLG) tasks demonstrate that LoRA-GGPO outperforms LoRA and its state-of-the-art variants. Furthermore, extended experiments specifically designed to analyze the double descent phenomenon confirm that LoRA-GGPO effectively alleviates this issue, producing more robust and generalizable models. Our work provides a robust and efficient solution for fine-tuning LLMs, with broad applicability in real-world scenarios. The code is available at https://github.com/llm172/LoRA-GGPO.

Large vision-language models (LVLMs) suffer from hallucination, resulting in misalignment between the output textual response and the input visual content. Recent research indicates that the over-reliance on the Large Language Model (LLM) backbone, as one cause of the LVLM hallucination, inherently introduces bias from language priors, leading to insufficient context attention to the visual inputs. We tackle this issue of hallucination by mitigating such over-reliance through preference learning. We propose Vision-guided Direct Preference Optimization (V-DPO) to enhance visual context learning at training time. To interpret the effectiveness and generalizability of V-DPO on different types of training data, we construct a synthetic dataset containing both response- and image-contrast preference pairs, compared against existing human-annotated hallucination samples. Our approach achieves significant improvements compared with baseline methods across various hallucination benchmarks. Our analysis indicates that V-DPO excels in learning from image-contrast preference data, demonstrating its superior ability to elicit and understand nuances of visual context. Our code is publicly available at https://github.com/YuxiXie/V-DPO.

Conversational Recommender Systems (CRSs) leverage natural language interactions for personalized recommendation, yet information-scarce dialogue histories and single-turn recommendation paradigms may severely hinder accurate modeling of complex user preferences. To alleviate this issue, recent studies have introduced LLM-based user simulators, which generate natural language feedback and perform simulated multi-turn interactions to assist recommendation. Nevertheless, since simulators cannot access true user preference labels during inference, their feedback may deviate from actual user interests, causing errors to accumulate over multiple interactions and severely affecting the generalization of the recommender. Inspired by the multi-step reasoning capabilities of LLMs and the effectiveness of reinforcement learning in policy optimization, we propose SMTPO, a user simulator-guided multi-turn preference optimization conversational recommendation framework. To align simulator-generated feedback with true user preferences in the absence of explicit labels, we enhance feedback quality via multi-task supervised fine-tuning (SFT), enabling the simulator to better reflect users' complex and diverse needs. To address the challenge of biased feedback destabilizing multi-turn optimization, we first allow the reasoning LLM-based recommender to learn preference reasoning and recommendation patterns through SFT and then employ reinforcement learning with fine-grained reward design to progressively align with true user preferences, improving recommendation performance. Extensive experiments on public datasets demonstrate the effectiveness and transferability of our method.

Large language model (LLM) agents now perform well on correctness-oriented repository-level tasks, including SWE-Bench issue resolution and feature implementation in real codebases. However, they still struggle with repository-level code optimization, which requires preserving behavior while improving runtime performance. Passing tests is not enough in this setting; a patch must preserve behavior, implement code optimization, and approach expert speedups. Current agents often miss bottlenecks hidden behind abstraction layers and native extensions, stop after shallow speedups, or insufficiently test the code patches that thus may silently break edge cases. We present PerfAgent, a profiler-guided, verifier-in-the-loop workflow that gives an off-the-shelf coding agent the feedback needed to find real hotspots, improve beyond the first passing patch, and use profiler evidence rather than timing alone to decide what to optimize next. On two challenging optimization benchmarks, GSO and SWE-fficiency-Lite, PerfAgent more than doubles the rate of expert-matching patches over OpenHands with GPT-5.1, improving from 19.6% to 39.2% on GSO and from 26% to 74% on SWE-fficiency-Lite. It also surpasses an oracle best-of-five baseline at substantially lower cost, showing that the gains come from better feedback rather than additional test-time sampling.

Recent progress in multi-turn reinforcement learning (RL) has significantly improved reasoning LLMs' performances on complex interactive tasks. Despite advances in stabilization techniques such as fine-grained credit assignment and trajectory filtering, instability remains pervasive and often leads to training collapse. We argue that this instability stems from inefficient exploration in multi-turn settings, where policies continue to generate low-information actions that neither reduce uncertainty nor advance task progress. To address this issue, we propose Token- and Turn-level Policy Optimization (T^2PO), an uncertainty-aware framework that explicitly controls exploration at fine-grained levels. At the token level, T^2PO monitors uncertainty dynamics and triggers a thinking intervention once the marginal uncertainty change falls below a threshold. At the turn level, T^2PO identifies interactions with negligible exploration progress and dynamically resamples such turns to avoid wasted rollouts. We evaluate T^2PO in diverse environments, including WebShop, ALFWorld, and Search QA, demonstrating substantial gains in training stability and performance improvements with better exploration efficiency. Code is available at: https://github.com/WillDreamer/T2PO.

Learning surfaces from neural radiance field (NeRF) became a rising topic in Multi-View Stereo (MVS). Recent Signed Distance Function (SDF)-based methods demonstrated their ability to reconstruct accurate 3D shapes of Lambertian scenes. However, their results on reflective scenes are unsatisfactory due to the entanglement of specular radiance and complicated geometry. To address the challenges, we propose a Gaussian-based representation of normals in SDF fields. Supervised by polarization priors, this representation guides the learning of geometry behind the specular reflection and captures more details than existing methods. Moreover, we propose a reweighting strategy in the optimization process to alleviate the noise issue of polarization priors. To validate the effectiveness of our design, we capture polarimetric information, and ground truth meshes in additional reflective scenes with various geometry. We also evaluated our framework on the PANDORA dataset. Comparisons prove our method outperforms existing neural 3D reconstruction methods in reflective scenes by a large margin.

Robotic manipulation is often challenging due to the long-horizon tasks and the complex object relationships. A common solution is to develop a task and motion planning framework that integrates planning for high-level task and low-level motion. Recently, inspired by the powerful reasoning ability of Large Language Models (LLMs), LLM-based planning approaches have achieved remarkable progress. However, these methods still heavily rely on expert-specific knowledge, often generating invalid plans for unseen and unfamiliar tasks. To address this issue, we propose an innovative language-guided symbolic task planning (LM-SymOpt) framework with optimization. It is the first expert-free planning framework since we combine the world knowledge from LLMs with formal reasoning, resulting in improved generalization capability to new tasks. Specifically, differ to most existing work, our LM-SymOpt employs LLMs to translate natural language instructions into symbolic representations, thereby representing actions as high-level symbols and reducing the search space for planning. Next, after evaluating the action probability of completing the task using LLMs, a weighted random sampling method is introduced to generate candidate plans. Their feasibility is assessed through symbolic reasoning and their cost efficiency is then evaluated using trajectory optimization for selecting the optimal planning. Our experimental results show that LM-SymOpt outperforms existing LLM-based planning approaches.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a scalable paradigm for improving the reasoning capabilities of large language models. However, its effectiveness is fundamentally limited by exploration: the policy can only improve on trajectories it has already sampled. While increasing the number of rollouts alleviates this issue, such brute-force scaling is computationally expensive, and existing approaches that modify the optimization objective provide limited control over what is explored. In this work, we propose NudgeRL, a framework for structured and diversity-driven exploration in RLVR. Our approach introduces Strategy Nudging, which conditions each rollout on lightweight, strategy-level contexts to induce diverse reasoning trajectories without relying on expensive oracle supervision. To effectively learn from such structured exploration, we further propose a unified objective, which decomposes the reward signal into inter- and intra-context components and incorporates a distillation objective to transfer discovered behaviors back to the base policy. Empirically, NudgeRL outperforms standard GRPO with up to 8 times larger rollout budgets, while outperforming oracle-guided RL baseline on average across five challenging math benchmarks. These results demonstrate that structured, context-driven exploration can serve as an efficient and scalable alternative to both brute-force rollout scaling and feasibility-oriented methods based on privileged information. Our code is available at https://github.com/tally0818/NudgeRL.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

Text-to-image diffusion models often struggle to achieve accurate semantic alignment between generated images and text prompts while maintaining efficiency for deployment on resource-constrained hardware. Existing approaches either incur substantial computational overhead through noise optimization or compromise semantic fidelity by aggressively pruning tokens. In this work, we propose OptiPrune, a unified framework that combines distribution-aware initial noise optimization with similarity-based token pruning to address both challenges simultaneously. Specifically, (1) we introduce a distribution-aware noise optimization module guided by attention scores to steer the initial latent noise toward semantically meaningful regions, mitigating issues such as subject neglect and feature entanglement; (2) we design a hardware-efficient token pruning strategy that selects representative base tokens via patch-wise similarity, injects randomness to enhance generalization, and recovers pruned tokens using maximum similarity copying before attention operations. Our method preserves the Gaussian prior during noise optimization and enables efficient inference without sacrificing alignment quality. Experiments on benchmark datasets, including Animal-Animal, demonstrate that OptiPrune achieves state-of-the-art prompt-image consistency with significantly reduced computational cost.

Large Language Models (LLMs) have demonstrated impressive progress in optimization modeling, fostering a rapid expansion of new methodologies and evaluation benchmarks. However, the boundaries of their capabilities in automated formulation and problem solving remain poorly understood, particularly when extending to complex, real-world tasks. To bridge this gap, we propose OPT-ENGINE, an extensible benchmark framework designed to evaluate LLMs on optimization modeling with controllable and scalable difficulty levels. OPT-ENGINE spans 10 canonical tasks across operations research, with five Linear Programming and five Mixed-Integer Programming. Utilizing OPT-ENGINE, we conduct an extensive study of LLMs' reasoning capabilities, addressing two critical questions: 1.) Do LLMs' performance remain robust when generalizing to out-of-distribution optimization tasks that scale in complexity beyond current benchmark levels? and 2.) At what stage, from problem interpretation to solution generation, do current LLMs encounter the most significant bottlenecks? Our empirical results yield two key insights: first, tool-integrated reasoning with external solvers exhibits significantly higher robustness as task complexity escalates, while pure-text reasoning reaches a ceiling; second, the automated formulation of constraints constitutes the primary performance bottleneck. These findings provide actionable guidance for developing next-generation LLMs for advanced optimization. Our code is publicly available at blue{https://github.com/Cardinal-Operations/OPTEngine}.

Optimization plays a vital role in scientific research and practical applications. However, formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise. We introduce OptimAI, a framework for solving Optimization problems described in natural language by leveraging LLM-powered AI agents, and achieve superior performance over current state-of-the-art methods. Our framework is built upon the following key roles: (1) a formulator that translates natural language problem descriptions into precise mathematical formulations; (2) a planner that constructs a high-level solution strategy prior to execution; and (3) a coder and a code critic capable of interacting with the environment and reflecting on outcomes to refine future actions. Ablation studies confirm that all roles are essential; removing the planner or code critic results in 5.8times and 3.1times drops in productivity, respectively. Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional 3.3times productivity gain. Our design emphasizes multi-agent collaboration, and our experiments confirm that combining diverse models leads to performance gains. Our approach attains 88.1% accuracy on the NLP4LP dataset and 82.3% on the Optibench dataset, reducing error rates by 58% and 52%, respectively, over prior best results.

In this paper, we present a method to optimize Gaussian splatting with a limited number of images while avoiding overfitting. Representing a 3D scene by combining numerous Gaussian splats has yielded outstanding visual quality. However, it tends to overfit the training views when only a small number of images are available. To address this issue, we introduce a dense depth map as a geometry guide to mitigate overfitting. We obtained the depth map using a pre-trained monocular depth estimation model and aligning the scale and offset using sparse COLMAP feature points. The adjusted depth aids in the color-based optimization of 3D Gaussian splatting, mitigating floating artifacts, and ensuring adherence to geometric constraints. We verify the proposed method on the NeRF-LLFF dataset with varying numbers of few images. Our approach demonstrates robust geometry compared to the original method that relies solely on images. Project page: robot0321.github.io/DepthRegGS

Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics that asks us to compute collision-free paths for a team of agents, all moving across a shared map. Although many works appear on this topic, all current algorithms struggle as the number of agents grows. The principal reason is that existing approaches typically plan free-flow optimal paths, which creates congestion. To tackle this issue, we propose a new approach for MAPF where agents are guided to their destination by following congestion-avoiding paths. We evaluate the idea in two large-scale settings: one-shot MAPF, where each agent has a single destination, and lifelong MAPF, where agents are continuously assigned new destinations. Empirically, we report large improvements in solution quality for one-short MAPF and in overall throughput for lifelong MAPF.

Motion generation is essential for animating virtual characters and embodied agents. While recent text-driven methods have made significant strides, they often struggle with achieving precise alignment between linguistic descriptions and motion semantics, as well as with the inefficiencies of slow, multi-step inference. To address these issues, we introduce TMR++ Aligned Preference Optimization (TAPO), an innovative framework that aligns subtle motion variations with textual modifiers and incorporates iterative adjustments to reinforce semantic grounding. To further enable real-time synthesis, we propose MotionFLUX, a high-speed generation framework based on deterministic rectified flow matching. Unlike traditional diffusion models, which require hundreds of denoising steps, MotionFLUX constructs optimal transport paths between noise distributions and motion spaces, facilitating real-time synthesis. The linearized probability paths reduce the need for multi-step sampling typical of sequential methods, significantly accelerating inference time without sacrificing motion quality. Experimental results demonstrate that, together, TAPO and MotionFLUX form a unified system that outperforms state-of-the-art approaches in both semantic consistency and motion quality, while also accelerating generation speed. The code and pretrained models will be released.

Diffusion prior-based methods have shown impressive results in real-world image super-resolution (ISR), yet two key challenges persist: balancing pixel-level fidelity with semantic quality, and adapting to diverse degradations. Existing dual-branch approaches freeze the pixel module during semantic training, but the semantic branch can still expand capacity within the pixel subspace, precluding genuine perceptual improvement. Moreover, using a single static adapter cannot generalize across heterogeneous real-world corruptions. To address both issues, we propose FreqOrtho-SR, which comprises: Frequency-guided Mixture of LoRA Experts (FreqMoE), it routes inputs to specialized experts via a non-parametric FFT-based degradation-feature extractor that encodes frequency-domain signatures, enabling stable and interpretable specialization across corruption types; and Orthogonal Gradient Projection (OGP), which reframes the dual-objective optimization as a subspace-constrained problem: by extracting the pixel-fidelity subspace via SVD on combined expert weight deltas and projecting semantic gradients onto its null space, OGP guarantees orthogonality between the two objectives, enabling genuinely complementary learning without mutual interference. Experiments show that FreqOrtho-SR achieves competitive overall performance and a strong fidelity-perception trade-off across multiple benchmarks with efficient single-step inference. The source code of our method can be found at https://github.com/sonhm3029/FreqOrtho-SR{sonhm3029/FreqOrtho-SR}.

Retrieval-augmented generation (RAG) substantially extends the knowledge boundary of large language models. However, it still faces two major challenges when handling complex reasoning tasks: low context utilization and frequent hallucinations. To address these issues, we propose Self-Correcting RAG, a unified framework that reformulates retrieval and generation as constrained optimization and path planning. On the input side, we move beyond traditional greedy retrieval and, for the first time, formalize context selection as a multi-dimensional multiple-choice knapsack problem (MMKP), thereby maximizing information density and removing redundancy under a strict token budget. On the output side, we introduce a natural language inference (NLI)-guided Monte Carlo Tree Search (MCTS) mechanism, which leverages test-time compute to dynamically explore reasoning trajectories and validate the faithfulness of generated answers. Experiments on six multi-hop question answering and fact-checking datasets demonstrate that our method significantly improves reasoning accuracy on complex queries while effectively reducing hallucinations, outperforming strong existing baselines.Our code is available at https://github.com/xjiacs/Self-Correcting-RAG .

Message passing neural networks (MPNNs) have emerged as go-to models for learning on graph-structured data in the past decade. Despite their effectiveness, most of such models still incur severe issues such as over-smoothing and -correlation, due to their underlying objective of minimizing the Dirichlet energy and the derived neighborhood aggregation operations. In this paper, we propose the DDSM, a new MPNN model built on an optimization framework that includes the stress majorization and orthogonal regularization for overcoming the above issues. Further, we introduce the diffusion distances for nodes into the framework to guide the new message passing operations and develop efficient algorithms for distance approximations, both backed by rigorous theoretical analyses. Our comprehensive experiments showcase that DDSM consistently and considerably outperforms 15 strong baselines on both homophilic and heterophilic graphs.

Navigating the capability--efficiency trade-off in Large Language Models (LLMs) requires approximating a high-quality Pareto set. Existing model merging research has focused predominantly on coarse model-level operators, which are easy to apply but offer limited control over the trade-off geometry. Layer-wise merging is more expressive, yet current methods still suffer from two bottlenecks: they treat the high-dimensional fusion space as an unstructured black box, and they rely on synchronous optimization despite highly uneven LLM evaluation latency. We propose Asynchronous Prior-guided Bayesian Model Merging (AP-BMM), which addresses these issues with a discrepancy-derived importance prior that initializes the surrogate geometry and an event-driven optimization loop built on pending-aware hypervolume improvement. Under a common evaluation budget, AP-BMM yields stronger Pareto-set approximations than both synchronous layer-wise baselines and representative model-level merging methods, with higher hypervolume and broader coverage of the trade-off frontier. Against the synchronous Bayesian baseline, it also achieves substantially shorter wall-clock time. Code: https://github.com/MiLab-HITSZ/AP-BMM.

In software maintenance, bug reproduction is essential for effective fault localization and repair. Manually writing reproduction scripts is a time-consuming task with high requirements for developers. Hence, automation of bug reproduction has increasingly attracted attention from researchers and practitioners. However, the existing studies on bug reproduction are generally limited to specific bug types such as program crashes, and hard to be applied to general bug reproduction. In this paper, considering the superior performance of agent-based methods in code intelligence tasks, we focus on designing an agent-based framework for the task. Directly employing agents would lead to limited bug reproduction performance, due to entangled subtasks, lengthy retrieved context, and unregulated actions. To mitigate the challenges, we propose an Automated gEneral buG reproductIon Scripts generation framework, named AEGIS, which is the first agent-based framework for the task. AEGIS mainly contains two modules: (1) A concise context construction module, which aims to guide the code agent in extracting structured information from issue descriptions, identifying issue-related code with detailed explanations, and integrating these elements to construct the concise context; (2) A FSM-based multi-feedback optimization module to further regulate the behavior of the code agent within the finite state machine (FSM), ensuring a controlled and efficient script generation process based on multi-dimensional feedback. Extensive experiments on the public benchmark dataset show that AEGIS outperforms the state-of-the-art baseline by 23.0% in F->P metric. In addition, the bug reproduction scripts generated by AEGIS can improve the relative resolved rate of Agentless by 12.5%.

Optimization is ubiquitous. While derivative-based algorithms have been powerful tools for various problems, the absence of gradient imposes challenges on many real-world applications. In this work, we propose Optimization by PROmpting (OPRO), a simple and effective approach to leverage large language models (LLMs) as optimizers, where the optimization task is described in natural language. In each optimization step, the LLM generates new solutions from the prompt that contains previously generated solutions with their values, then the new solutions are evaluated and added to the prompt for the next optimization step. We first showcase OPRO on linear regression and traveling salesman problems, then move on to prompt optimization where the goal is to find instructions that maximize the task accuracy. With a variety of LLMs, we demonstrate that the best prompts optimized by OPRO outperform human-designed prompts by up to 8% on GSM8K, and by up to 50% on Big-Bench Hard tasks.

Conditional image generation enhances text-to-image synthesis with structural, spatial, or stylistic priors, but current methods face challenges in handling conflicts between sources. These include 1) input-level conflicts, where the conditioning image contradicts the text prompt, and 2) model-bias conflicts, where generative biases disrupt alignment even when conditions match the text. Addressing these conflicts requires nuanced solutions, which standard supervised fine-tuning struggles to provide. Preference-based optimization techniques like Direct Preference Optimization (DPO) show promise but are limited by gradient entanglement between text and condition signals and lack disentangled training data for multi-constraint tasks. To overcome this, we propose a bidirectionally decoupled DPO framework (BideDPO). Our method creates two disentangled preference pairs-one for the condition and one for the text-to reduce gradient entanglement. The influence of pairs is managed using an Adaptive Loss Balancing strategy for balanced optimization. We introduce an automated data pipeline to sample model outputs and generate conflict-aware data. This process is embedded in an iterative optimization strategy that refines both the model and the data. We construct a DualAlign benchmark to evaluate conflict resolution between text and condition. Experiments show BideDPO significantly improves text success rates (e.g., +35%) and condition adherence. We also validate our approach using the COCO dataset. Project Pages: https://limuloo.github.io/BideDPO/.

Scaling LLM-based optimization from textbook-scale instances to real-world, industrial tasks remains a critical open challenge. Existing approaches are predominantly evaluated on small, self-contained textual problems and often commit to a solver-integrated paradigm, limiting their ability to handle the scale and structural diversity of practical optimization workloads. In this work, we propose a practical framework for training open-source LLMs to tackle real-world, industrial-scale optimization. We first show empirically that solver-integrated reasoning, exact combinatorial algorithm, and heuristic search exhibit complementary strengths across different problem structures and scales. Motivated by this, we introduce Strategy-Diverse Reinforcement Learning (SDRL), which trains LLMs as adaptive optimization meta-solvers. SDRL leverages this complementarity through a correctness-gated hierarchical diversity reward that promotes robust exploration across varying strategies and within each strategy, effectively preventing premature strategy collapse. We further introduce a mixed-format training scheme that jointly supports both self-contained textual problems and file-grounded instances. Across comprehensive evaluations, our framework outperforms existing fine-tuned methods and frontier models including DeepSeek-V4-Pro and GPT-5.5, both on average across benchmarks and on industrial-scale optimization tasks.

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.

Optimization Modeling (OM) is essential for solving complex decision-making problems. However, the process remains time-consuming and error-prone, heavily relying on domain experts. While Large Language Models (LLMs) show promise in addressing these challenges through their natural language understanding and reasoning capabilities, current approaches face three critical limitations: high benchmark labeling error rates reaching up to 42%, narrow evaluation scope that only considers optimal values, and computational inefficiency due to heavy reliance on multi-agent systems or model fine-tuning. In this work, we first enhance existing datasets through systematic error correction and more comprehensive annotation. Additionally, we introduce LogiOR, a new optimization modeling benchmark from the logistics domain, containing more complex problems with standardized annotations. Furthermore, we present ORThought, a novel framework that leverages expert-level optimization modeling principles through chain-of-thought reasoning to automate the OM process. Through extensive empirical evaluation, we demonstrate that ORThought outperforms existing approaches, including multi-agent frameworks, with particularly significant advantages on complex optimization problems. Finally, we provide a systematic analysis of our method, identifying critical success factors and failure modes, providing valuable insights for future research on LLM-based optimization modeling.

Reinforcement Learning, particularly through policy gradient methods, has played a central role in enabling reasoning capabilities of Large Language Models. However, the optimization stability of policy gradients in this setting remains understudied. As a result, existing implementations often resort to conservative hyperparameter choices to ensure stability, which requires more training samples and increases computational costs. Hence, developing models for reliably tracking the underlying optimization dynamics and leveraging them into training enables more sample-efficient regimes and further unleashes scalable post-training. We address this gap by formalizing the stochastic optimization problem of policy gradients with explicit consideration of second-order geometry. We propose a tractable computational framework that tracks and leverages curvature information during policy updates. We further employ this framework to design interventions in the optimization process through data selection. The resultant algorithm, Curvature-Aware Policy Optimization (CAPO), identifies samples that contribute to unstable updates and masks them out. Theoretically, we establish monotonic improvement guarantees under realistic assumptions. On standard math reasoning benchmarks, we empirically show that CAPO ensures stable updates under aggressive learning regimes where baselines catastrophically fail. With minimal intervention (rejecting fewer than 8% of tokens), CAPO achieves up to 30x improvement in sample efficiency over standard GRPO for LLM reasoning.

Although LLM-based agents have attracted significant attention in domains such as software engineering and machine learning research, their role in advancing combinatorial optimization (CO) remains relatively underexplored. This gap underscores the need for a deeper understanding of their potential in tackling structured, constraint-intensive problems-a pursuit currently limited by the absence of comprehensive benchmarks for systematic investigation. To address this, we introduce CO-Bench, a benchmark suite featuring 36 real-world CO problems drawn from a broad range of domains and complexity levels. CO-Bench includes structured problem formulations and curated data to support rigorous investigation of LLM agents. We evaluate multiple agent frameworks against established human-designed algorithms, revealing key strengths and limitations of current approaches and identifying promising directions for future research. CO-Bench is publicly available at https://github.com/sunnweiwei/CO-Bench.

Large Language Models (LLMs) have already been widely adopted for automated algorithm design, demonstrating strong abilities in generating and evolving algorithms across various fields. Existing work has largely focused on examining their effectiveness in solving specific problems, with search strategies primarily guided by adaptive prompt designs. In this paper, through investigating the token-wise attribution of the prompts to LLM-generated algorithmic codes, we show that providing high-quality algorithmic code examples can substantially improve the performance of the LLM-driven optimization. Building upon this insight, we propose leveraging prior benchmark algorithms to guide LLM-driven optimization and demonstrate superior performance on two black-box optimization benchmarks: the pseudo-Boolean optimization suite (pbo) and the black-box optimization suite (bbob). Our findings highlight the value of integrating benchmarking studies to enhance both efficiency and robustness of the LLM-driven black-box optimization methods.

Tackling complex optimization problems often relies on expert-designed heuristics, typically crafted through extensive trial and error. Recent advances demonstrate that large language models (LLMs), when integrated into well-designed evolutionary search frameworks, can autonomously discover high-performing heuristics at a fraction of the traditional cost. However, existing approaches predominantly rely on verbal guidance, i.e., manipulating the prompt generation process, to steer the evolution of heuristics, without adapting the underlying LLM. We propose a hybrid framework that combines verbal and numerical guidance, the latter achieved by fine-tuning the LLM via reinforcement learning based on the quality of generated heuristics. This joint optimization allows the LLM to co-evolve with the search process. Our method outperforms state-of-the-art (SOTA) baselines across various optimization tasks, running locally on a single 24GB GPU using a 7B model with INT4 quantization. It surpasses methods that rely solely on verbal guidance, even when those use significantly more powerful API-based models.

Recent systems for optimizing prompts, programs, and ML workflows typically rely on explicit outer-loop controllers such as evolutionary search, bandits, or textual-gradient methods. We ask a fundamentally different question: how much of this search policy can be internalized by a single tool-using agent? We present ReASearch, a unified framework for reasoning-driven optimization in which the agent autonomously decides what to evaluate, how to diagnose failures, which edits to make, and when to verify or restart. Rather than serving only as a proposal generator guided by hand-designed heuristics, the agent actively analyzes outcomes, allocates budget, and refines its strategy over long horizons through persistent memory. With a shared agent loop and domain-specific tools, ReASearch instantiates the exact same scaffold to optimize prompts, programs, and ML workflows. Across 14 diverse tasks, it is competitive with and mostly better than specialized optimization systems, achieving gains of 2% to 40% over strong domain-specific baselines, and in some cases discovering solutions that improve on prior human best-known results. Crucially, we observe that complex search behaviors, which are typically implemented by explicit controllers, emerge naturally from the agent's reasoning process.

While Large Language Models (LLMs) demonstrate remarkable reasoning, complex optimization tasks remain challenging, requiring domain knowledge and robust implementation. However, existing benchmarks focus narrowly on Mathematical Programming and Combinatorial Optimization, hindering comprehensive evaluation. To address this, we introduce OptiVerse, a comprehensive benchmark of 1,000 curated problems spanning neglected domains, including Stochastic Optimization, Dynamic Optimization, Game Optimization, and Optimal Control, across three difficulty levels: Easy, Medium, and Hard. The experiments with 22 LLMs of different sizes reveal sharp performance degradation on hard problems, where even advanced models like GPT-5.2 and Gemini-3 struggle to exceed 27% accuracy. Through error analysis, we identify that modeling & logic errors remain the primary bottleneck. Consequently, we propose a Dual-View Auditor Agent that improves the accuracy of the LLM modeling process without introducing significant time overhead. OptiVerse will serve as a foundational platform for advancing LLMs in solving complex optimization challenges.

Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. This paper introduces OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. OptiMUS can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve its model and code based on these evaluations. OptiMUS utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS outperforms existing state-of-the-art methods on easy datasets by more than 20% and on hard datasets (including a new dataset, NLP4LP, released with this paper that features long and complex problems) by more than 30%.

Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data, incurring significant computational cost. Existing learning-based methods require training dedicated models for each problem distribution, for each downstream task, severely limiting their scalability and generalization. We introduce Forge: Foundational Optimization Representations from Graph Embeddings, a framework that pre-trains a vector-quantized graph autoencoder on a large, diverse collection of mixed-integer programming (MIP) instances in an unsupervised manner, without relying on optimization solvers or optimal solutions. Vector quantization produces discrete code assignments that serve as a vocabulary for representing optimization instances. We evaluate Forge in both unsupervised and supervised settings. In the unsupervised setting, Forge embeddings effectively cluster unseen instances across problem domains and sizes. In the supervised setting, we fine-tune Forge embeddings and show that a single pre-trained model helps predicting both the integrality gap for cut-generation and variable hints for search guidance across multiple problem and size distributions. In both tasks, we improve the performance of a commercial optimization solver and outperform state-of-the-art learning-based methods. Finally, we open-source our training code, pre-trained Forge weights, and embeddings for multiple MIP distributions to foster further research in representation learning for optimization problems.

Large Language Models (LLMs) have shown remarkable capabilities in solving various programming tasks, such as code generation. However, their potential for code optimization, particularly in performance enhancement, remains largely unexplored. This paper investigates the capabilities of LLMs in optimizing code for minimal execution time, addressing a critical gap in current research. The recently proposed code optimization methods construct program optimization pairs based on iterative submissions from the same programmer for the same problem. However, this approach confines LLMs to local performance improvements, neglecting global algorithmic innovation. To overcome this limitation, we adopt a completely different perspective by reconstructing the optimization pairs into a problem-oriented approach. This allows for the integration of various ideas from multiple programmers tackling the same problem. Furthermore, we observe that code optimization presents greater challenges compared to code generation, often accompanied by "optimization tax". Recognizing the inherent trade-offs in correctness and efficiency, we introduce a novel anchor verification framework to mitigate this "optimization tax". Ultimately, the problem oriented perspective combined with the anchor verification framework significantly enhances both the correct optimization ratio and speedup to new levels.

There is growing interest in utilizing large language models (LLMs) as co-pilots for combinatorial optimization and constraint programming tasks across various problems. This paper aims to advance this line of research by introducing Text2Zinc}, a cross-domain dataset for capturing optimization and satisfaction problems specified in natural language text. Our work is distinguished from previous attempts by integrating both satisfaction and optimization problems within a unified dataset using a solver-agnostic modeling language. To achieve this, we leverage MiniZinc's solver-and-paradigm-agnostic modeling capabilities to formulate these problems. Using the Text2Zinc dataset, we conduct comprehensive baseline experiments to compare execution and solution accuracy across several methods, including off-the-shelf prompting strategies, chain-of-thought reasoning, and a compositional approach. Additionally, we explore the effectiveness of intermediary representations, specifically knowledge graphs. Our findings indicate that LLMs are not yet a push-button technology to model combinatorial problems from text. We hope that Text2Zinc serves as a valuable resource for researchers and practitioners to advance the field further.

While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO) -- searching high-dimensional solution spaces under hard constraints -- remains underexplored. To bridge the gap, we introduce NLCO, a Natural Language Combinatorial Optimization benchmark that evaluates LLMs on end-to-end CO reasoning: given a language-described decision-making scenario, the model must output a discrete solution without writing code or calling external solvers. NLCO covers 43 CO problems and is organized using a four-layer taxonomy of variable types, constraint families, global patterns, and objective classes, enabling fine-grained evaluation. We provide solver-annotated solutions and comprehensively evaluate LLMs by feasibility, solution optimality, and reasoning efficiency. Experiments across a wide range of modern LLMs show that high-performing models achieve strong feasibility and solution quality on small instances, but both degrade as instance size grows, even if more tokens are used for reasoning. We also observe systematic effects across the taxonomy: set-based tasks are relatively easy, whereas graph-structured problems and bottleneck objectives lead to more frequent failures.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Optimization modeling is fundamental to decision-making across diverse domains.Despite progress in automating optimization formulation from natural language descriptions, Large Language Models (LLMs) often struggle to generate formally correct and usable models due to hallucinations, posing a challenge for reliable automation. Inspired by the success of Reinforcement Learning (RL) in enhancing Large Reasoning Models, we present Solver-Informed Reinforcement Learning (SIRL).This novel framework leverages external optimization solvers as verifiable reward mechanisms to significantly improve the authenticity of LLMs for optimization modeling.Acting as precise verifiers, these solvers automatically assess the executable code and the instance-level mathematical model represented by the associated LP file, yielding precise and comprehensive feedback signals -- including syntax, feasibility, and solution quality that directly inform the RL process. This automated verification process, powered by classic optimization solvers, also underpins our instance-enhanced self-consistency method to synthesize high-quality training data. Extensive experiments on diverse public benchmarks demonstrate that SIRL achieves state-of-the-art performance, substantially outperforming existing methods in generating accurate and executable optimization models.

Issue resolution, a complex Software Engineering (SWE) task integral to real-world development, has emerged as a compelling challenge for artificial intelligence. The establishment of benchmarks like SWE-bench revealed this task as profoundly difficult for large language models, thereby significantly accelerating the evolution of autonomous coding agents. This paper presents a systematic survey of this emerging domain. We begin by examining data construction pipelines, covering automated collection and synthesis approaches. We then provide a comprehensive analysis of methodologies, spanning training-free frameworks with their modular components to training-based techniques, including supervised fine-tuning and reinforcement learning. Subsequently, we discuss critical analyses of data quality and agent behavior, alongside practical applications. Finally, we identify key challenges and outline promising directions for future research. An open-source repository is maintained at https://github.com/DeepSoftwareAnalytics/Awesome-Issue-Resolution to serve as a dynamic resource in this field.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

Automatic Prompt Optimization (APO) is a powerful approach for extracting performance from large language models without modifying their weights. Many existing methods rely on trial-and-error, testing different prompts or in-context examples until a good configuration emerges, often consuming substantial compute. Recently, natural language feedback derived from execution logs has shown promise as a way to identify how prompts can be improved. However, most prior approaches operate in a bottom-up manner, iteratively adjusting the prompt based on feedback from individual problems, which can cause them to lose the global perspective. In this work, we propose Error Taxonomy-Guided Prompt Optimization (ETGPO), a prompt optimization algorithm that adopts a top-down approach. ETGPO focuses on the global failure landscape by collecting model errors, categorizing them into a taxonomy, and augmenting the prompt with guidance targeting the most frequent failure modes. Across multiple benchmarks spanning mathematics, question answering, and logical reasoning, ETGPO achieves accuracy that is comparable to or better than state-of-the-art methods, while requiring roughly one third of the optimization-phase token usage and evaluation budget.

We study the potential of using large language models (LLMs) as an interactive optimizer for solving maximization problems in a text space using natural language and numerical feedback. Inspired by the classical optimization literature, we classify the natural language feedback into directional and non-directional, where the former is a generalization of the first-order feedback to the natural language space. We find that LLMs are especially capable of optimization when they are provided with {directional feedback}. Based on this insight, we design a new LLM-based optimizer that synthesizes directional feedback from the historical optimization trace to achieve reliable improvement over iterations. Empirically, we show our LLM-based optimizer is more stable and efficient in solving optimization problems, from maximizing mathematical functions to optimizing prompts for writing poems, compared with existing techniques.

Optimization problems are pervasive across various sectors, from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve MILP problems from their natural language descriptions. OptiMUS is capable of developing mathematical models, writing and debugging solver code, developing tests, and checking the validity of generated solutions. To benchmark our agent, we present NLP4LP, a novel dataset of linear programming (LP) and mixed integer linear programming (MILP) problems. Our experiments demonstrate that OptiMUS solves nearly twice as many problems as a basic LLM prompting strategy. OptiMUS code and NLP4LP dataset are available at https://github.com/teshnizi/OptiMUS{https://github.com/teshnizi/OptiMUS}

Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning. Solving realistic optimization (OPT) problems in application scenarios requires advanced and applied mathematics ability. However, current OPT benchmarks that merely solve linear programming are far from complex realistic situations. In this work, we propose OptiBench, a benchmark for End-to-end optimization problem-solving with human-readable inputs and outputs. OptiBench contains rich optimization problems, including linear and nonlinear programming with or without tabular data, which can comprehensively evaluate LLMs' solving ability. In our benchmark, LLMs are required to call a code solver to provide precise numerical answers. Furthermore, to alleviate the data scarcity for optimization problems, and to bridge the gap between open-source LLMs on a small scale (e.g., Llama-3-8b) and closed-source LLMs (e.g., GPT-4), we further propose a data synthesis method namely ReSocratic. Unlike general data synthesis methods that proceed from questions to answers, \ReSocratic first incrementally synthesizes formatted optimization demonstration with mathematical formulations step by step and then back-translates the generated demonstrations into questions. Based on this, we synthesize the ReSocratic-29k dataset. We further conduct supervised fine-tuning with ReSocratic-29k on multiple open-source models. Experimental results show that ReSocratic-29k significantly improves the performance of open-source models.

Recent advances in formal theorem proving have focused on Olympiad-level mathematics, leaving undergraduate domains largely unexplored. Optimization, fundamental to machine learning, operations research, and scientific computing, remains underserved by existing provers. Its reliance on domain-specific formalisms (convexity, optimality conditions, and algorithmic analysis) creates significant distribution shift, making naive domain transfer ineffective. We present OptProver, a trained model that achieves robust transfer from Olympiad to undergraduate optimization. Starting from a strong Olympiad-level prover, our pipeline mitigates distribution shift through two key innovations. First, we employ large-scale optimization-focused data curation via expert iteration. Second, we introduce a specialized preference learning objective that integrates perplexity-weighted optimization with a mechanism to penalize valid but non-progressing proof steps. This not only addresses distribution shifts but also guides the search toward efficient trajectories. To enable rigorous evaluation, we construct a novel benchmark in Lean 4 focused on optimization. On this benchmark, OptProver achieves state-of-the-art Pass@1 and Pass@32 among comparably sized models while maintaining competitive performance on general theorem-proving tasks, demonstrating effective domain transfer without catastrophic forgetting.

Text-to-optimization requires two separable capabilities: modeling -- choosing the right optimization structure -- and binding -- grounding every coefficient, index, and parameter in the concrete problem data. We study this via Text2Opt-Bench, a scalable benchmark of solver-verified optimization problems spanning 12 categories, from textbook linear programs to stochastic and multi-objective formulations with up to thousands of variables. Across 10+ models, we find that accuracy collapses as instance data grows, even when the formulation itself is simple. We call this the effective binding limit. We address this via a simple inference-time approach, BIND, which externalizes numeric data to structured files so the model binds data programmatically rather than transcribing from the prompt. BIND improves GPT-5-Nano from 59.1% to 82.4% accuracy, matching pass@5 (82.0%) at lower token cost than pass@1, and GPT-5 from 86.2% to 95.8%. Furthermore, we validate our hypothesis by finetuning a model exclusively on binding and show that it outperforms end-to-end SFT and RL across three structurally distinct optimization categories, with a 1.5B binding specialist alone matching a 7B end-to-end baseline.

Large language models (LLMs) are increasingly deployed as agents that rely on system prompts to use tools and complete tasks. Such deployments impose distinct operational requirements, including appropriate tool use, concise prompts and solution paths, and compliance with safety and formatting policies. For many practitioners, however, assembling domain-specific supervised data to post-train models to meet these requirements is infeasible. We introduce CAPO (Constraint-Aware Prompt Optimization), a primal-dual method that combines pool-based rewrites with adaptive constraint weighting to optimize system prompts under explicit operational constraints. Across agentic benchmarks, CAPO more reliably reaches empirically feasible operating points while improving task performance. CAPO also generalizes beyond agentic settings, achieving strong results on assistant-style evaluations with output-format and safety/privacy constraints. We further introduce DCAPO (Dynamically Trained CAPO), which trains a feedback- and dual-conditioned rewriter with pool-based GRPO while keeping the task agent frozen. Across task agents of different sizes, DCAPO produces a feasible prompt in every evaluated domain and matches or improves the task accuracy achieved by the evaluated baselines. A surrogate analysis characterizes how finite-pool and discrete-rewrite errors enter the inexact primal-dual procedure.

Many real-world optimization problems are guided by complex, subjective preferences that are difficult to express as explicit closed-form objectives. In response, we introduce Language-in-the-Loop Optimization (LILO), a Bayesian optimization (BO) framework that employs a large language model (LLM) to translate free-form natural language feedback and prior knowledge from a decision maker into structured preference signals, going beyond the restrictive scalar or pairwise feedback formats typically assumed in preferential BO. The LLM-derived preferences are integrated by a Gaussian process proxy model, enabling principled acquisition-driven exploration with calibrated uncertainty. By placing the LLM in a supporting role rather than as the optimizer itself, LILO preserves the sample efficiency and stability of BO while providing a flexible and expressive feedback interface. Across synthetic and real-world benchmarks, LILO consistently outperforms both conventional preference-based BO methods and LLM-only optimizers, with particularly strong gains in feedback-limited regimes.

Large language models (LLMs) are increasingly used to formulate optimization models from natural-language problem descriptions, yet realistic operations research (OR) requests are often incomplete: missing objectives, constraints, or business rules can change the resulting mathematical program. Existing evaluations largely assume a complete specification and therefore overlook whether an agent knows when clarification is needed before modeling. We introduce OR-Clarify, a benchmark for pre-formulation clarification. Each task presents a partial public problem description, withholds structured hidden slots, and evaluates agents through bounded interaction with a simulated user. The benchmark supports both openended and choice-based clarification, and measures slot recovery, stopping behavior, silent assumptions, and interaction cost. We further propose Interactive Optimization (InterOPT), a two-stage framework that identifies unresolved formulation-critical gaps and uses them to guide whether to ask the next question or to stop. In our choice-based experiments, InterOPT substantially outperforms all baselines in exact slot recovery; in the open-ended setting, it remains competitive with strong prior methods. Together, OR-Clarify and InterOPT reframe OR assistance as a selective completeness decision: clarify when needed, stop when ready, and quantify what remains missing.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.

Offline preference optimization is a key method for enhancing and controlling the quality of Large Language Model (LLM) outputs. Typically, preference optimization is approached as an offline supervised learning task using manually-crafted convex loss functions. While these methods are based on theoretical insights, they are inherently constrained by human creativity, so the large search space of possible loss functions remains under explored. We address this by performing LLM-driven objective discovery to automatically discover new state-of-the-art preference optimization algorithms without (expert) human intervention. Specifically, we iteratively prompt an LLM to propose and implement new preference optimization loss functions based on previously-evaluated performance metrics. This process leads to the discovery of previously-unknown and performant preference optimization algorithms. The best performing of these we call Discovered Preference Optimization (DiscoPOP), a novel algorithm that adaptively blends logistic and exponential losses. Experiments demonstrate the state-of-the-art performance of DiscoPOP and its successful transfer to held-out tasks.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Optimization can be found in many real-life applications. Designing an effective algorithm for a specific optimization problem typically requires a tedious amount of effort from human experts with domain knowledge and algorithm design skills. In this paper, we propose a novel approach called Algorithm Evolution using Large Language Model (AEL). It utilizes a large language model (LLM) to automatically generate optimization algorithms via an evolutionary framework. AEL does algorithm-level evolution without model training. Human effort and requirements for domain knowledge can be significantly reduced. We take constructive methods for the salesman traveling problem as a test example, we show that the constructive algorithm obtained by AEL outperforms simple hand-crafted and LLM-generated heuristics. Compared with other domain deep learning model-based algorithms, these methods exhibit excellent scalability across different problem sizes. AEL is also very different from previous attempts that utilize LLMs as search operators in algorithms.

Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains challenging for current large language models (LLMs). In this paper, we propose Agora-Opt, a modular agentic framework for optimization modeling that combines decentralized debate with a read-write memory bank. Agora-Opt allows multiple agent teams to independently produce end-to-end solutions and reconcile them through an outcome-grounded debate protocol, while memory stores solver-verified artifacts and past disagreement resolutions to support training-free improvement over time. This design is flexible across both backbones and methods: it reduces base-model lock-in, transfers across different LLM families, and can be layered onto existing pipelines with minimal coupling. Across public benchmarks, Agora-Opt achieves the strongest overall performance among all compared methods, outperforming strong zero-shot LLMs, training-centric approaches, and prior agentic baselines. Further analyses show robust gains across backbone choices and component variants, and demonstrate that decentralized debate offers a structural advantage over centralized selection by enabling agents to refine candidate solutions through interaction and even recover correct formulations when all initial candidates are flawed. These results suggest that reliable optimization modeling benefits from combining collaborative cross-checking with reusable experience, and position Agora-Opt as a practical and extensible foundation for trustworthy optimization modeling assistance. Our code and data are available at https://github.com/CHIANGEL/Agora-Opt.

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.

Prompt optimization (PO) offers a practical alternative to fine-tuning large language models (LLMs), enabling performance improvements without altering model weights. Existing methods typically rely on advanced, large-scale LLMs like GPT-4 to generate optimized prompts. However, due to limited downward compatibility, verbose, instruction-heavy prompts from advanced LLMs can overwhelm lightweight inference models and degrade response quality. In this work, we rethink prompt optimization through the lens of interpretable design. We first identify a set of model-agnostic prompt quality merits and empirically validate their effectiveness in enhancing prompt and response quality. We then introduce MePO, a merit-guided, lightweight, and locally deployable prompt optimizer trained on our preference dataset built from merit-aligned prompts generated by a lightweight LLM. Unlike prior work, MePO avoids online optimization reliance, reduces cost and privacy concerns, and, by learning clear, interpretable merits, generalizes effectively to both large-scale and lightweight inference models. Experiments demonstrate that MePO achieves better results across diverse tasks and model types, offering a scalable and robust solution for real-world deployment. Our model and dataset are available at: https://github.com/MidiyaZhu/MePO

Optimization underpins decision-making in domains from healthcare to logistics, yet for many practitioners it remains a "magical box": powerful but opaque, difficult to use, and reliant on specialized expertise. While prior work has extensively studied machine learning workflows, the everyday practices of optimization model developers (OMDs) have received little attention. We conducted semi-structured interviews with 15 OMDs across diverse domains to examine how optimization is done in practice. Our findings reveal a highly iterative workflow spanning six stages: problem elicitation, data processing, model development, implementation, validation, and deployment. Importantly, we find that optimization practice is not only about algorithms that deliver better decisions, but is equally shaped by data and dialogue - the ongoing communication with stakeholders that enables problem framing, trust, and adoption. We discuss opportunities for future tooling that foregrounds data and dialogue alongside decision-making, opening new directions for human-centered optimization.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

The Natural Language for Optimization (NL4Opt) Competition was created to investigate methods of extracting the meaning and formulation of an optimization problem based on its text description. Specifically, the goal of the competition is to increase the accessibility and usability of optimization solvers by allowing non-experts to interface with them using natural language. We separate this challenging goal into two sub-tasks: (1) recognize and label the semantic entities that correspond to the components of the optimization problem; (2) generate a meaning representation (i.e., a logical form) of the problem from its detected problem entities. The first task aims to reduce ambiguity by detecting and tagging the entities of the optimization problems. The second task creates an intermediate representation of the linear programming (LP) problem that is converted into a format that can be used by commercial solvers. In this report, we present the LP word problem dataset and shared tasks for the NeurIPS 2022 competition. Furthermore, we investigate and compare the performance of the ChatGPT large language model against the winning solutions. Through this competition, we hope to bring interest towards the development of novel machine learning applications and datasets for optimization modeling.

Optimization modeling enables critical decisions across industries but remains difficult to automate: informal language must be mapped to precise mathematical formulations and executable solver code. Prior LLM approaches either rely on brittle prompting or costly retraining with limited generalization. We present AlphaOPT, a self-improving experience library that enables an LLM to learn from limited demonstrations (even answers alone, without gold-standard programs) and solver feedback - without annotated reasoning traces or parameter updates. AlphaOPT operates in a continual two-phase cycle: (i) a Library Learning phase that reflects on failed attempts, extracting solver-verified, structured insights as {taxonomy, condition, explanation, example}; and (ii) a Library Evolution phase that diagnoses retrieval misalignments and refines the applicability conditions of stored insights, improving transfer across tasks. This design (1) learns efficiently from limited demonstrations without curated rationales, (2) expands continually without costly retraining by updating the library rather than model weights, and (3) makes knowledge explicit and interpretable for human inspection and intervention. Experiments show that AlphaOPT steadily improves with more data (65% to 72% from 100 to 300 training items) and surpasses the strongest baseline by 7.7% on the out-of-distribution OptiBench dataset when trained only on answers. Code and data are available at: https://github.com/Minw913/AlphaOPT.

Optimization modeling via mixed-integer linear programming (MILP) is fundamental to industrial planning and scheduling, yet translating natural-language requirements into solver-executable models and maintaining them under evolving business rules remains highly expertise-intensive. While large language models (LLMs) offer promising avenues for automation, existing methods often suffer from low data efficiency, limited solver-level validity, and poor scalability to industrial-scale problems. To address these challenges, we present EvoOpt-LLM, a unified LLM-based framework supporting the full lifecycle of industrial optimization modeling, including automated model construction, dynamic business-constraint injection, and end-to-end variable pruning. Built on a 7B-parameter LLM and adapted via parameter-efficient LoRA fine-tuning, EvoOpt-LLM achieves a generation rate of 91% and an executability rate of 65.9% with only 3,000 training samples, with critical performance gains emerging under 1,500 samples. The constraint injection module reliably augments existing MILP models while preserving original objectives, and the variable pruning module enhances computational efficiency, achieving an F1 score of ~0.56 on medium-sized LP models with only 400 samples. EvoOpt-LLM demonstrates a practical, data-efficient approach to industrial optimization modeling, reducing reliance on expert intervention while improving adaptability and solver efficiency.

Discrete text-trigger optimization -- searching for text sequences that, when ingested by a model, steer it toward a specified objective -- underpins model red-teaming (e.g., LLM jailbreaks), as well as auditing and interpretability. However, the current state of discrete optimizers hinders their adoption and progress. First, existing optimizers, when open-sourced at all, are scattered across research codebases tied to specific models, objectives, and problem domains. Second, optimizer variants proliferate, each requiring engineering overhead to use or extend, and remaining hard to compare head-to-head. Together, these raise the bar for adopting optimizers in existing or new domains, and for advancing them via new strategies. We address these gaps with TROPT, the first open-source framework that unifies discrete optimizers' execution and standardizes their development under a single interface. TROPT makes it easy to customize end-to-end optimization recipes by swapping any component -- models, objectives, and optimizers -- extending its reach across domains and new applications. TROPT currently ships with 30+ optimization recipes -- covering applications such as jailbreaking and probing model internals -- built from 15+ optimizers (spanning white-box to black-box access) and 15+ losses, from foundational to state-of-the-art methods. Demonstrating its utility, we leverage TROPT in several studies: (i) controlled, large-scale experiments comparing and enhancing optimization strategies for LLM jailbreaks, revealing potent-yet-underadopted techniques; and (ii) porting optimizers from one domain (e.g., LLM jailbreak) to new domains (e.g., corpus-poisoning embedding model). In all, TROPT significantly lowers the barrier to adopting and advancing discrete text optimization.

LLM routing aims to select the most appropriate model for each query, balancing competing performance metrics such as accuracy and cost across a pool of language models. Prior approaches typically adopt a decoupled strategy, where the metrics are first predicted and the model is then selected based on these estimates. This setup is prone to compounding errors and often relies on full-feedback data, where each query is evaluated by all candidate models, which is costly to obtain and maintain in practice. In contrast, we learn from observational data, which records only the outcome of the model actually deployed. We propose a causal end-to-end framework that learns routing policies by minimizing decision-making regret from observational data. To enable efficient optimization, we introduce two theoretically grounded surrogate objectives: a classification-based upper bound, and a softmax-weighted regret approximation shown to recover the optimal policy at convergence. We further extend our framework to handle heterogeneous cost preferences via an interval-conditioned architecture. Experiments on public benchmarks show that our method outperforms existing baselines, achieving state-of-the-art performance across different embedding models.

Reinforcement learning exhibits potential in enhancing the reasoning abilities of large language models, yet it is hard to scale for the low sample efficiency during the rollout phase. Existing methods attempt to improve efficiency by scheduling problems based on problem difficulties. However, these approaches suffer from unstable and biased estimations of problem difficulty and fail to capture the alignment between model competence and problem difficulty in RL training, leading to suboptimal results. To tackle these limitations, this paper introduces Competence-Difficulty Alignment Sampling (CDAS), which enables accurate and stable estimation of problem difficulties by aggregating historical performance discrepancies of problems. Then the model competence is quantified to adaptively select problems whose difficulty is in alignment with the model's current competence using a fixed-point system. Experimental results across a range of challenging mathematical benchmarks show that CDAS achieves great improvements in both accuracy and efficiency. CDAS attains the highest average accuracy against baselines and exhibits significant speed advantages compared to Dynamic Sampling, a competitive strategy in DAPO, which is 2.33 times slower than CDAS.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Optimization plays a costly and crucial role in developing machine learning systems. In learned optimizers, the few hyperparameters of commonly used hand-designed optimizers, e.g. Adam or SGD, are replaced with flexible parametric functions. The parameters of these functions are then optimized so that the resulting learned optimizer minimizes a target loss on a chosen class of models. Learned optimizers can both reduce the number of required training steps and improve the final test loss. However, they can be expensive to train, and once trained can be expensive to use due to computational and memory overhead for the optimizer itself. In this work, we identify and quantify the design features governing the memory, compute, and performance trade-offs for many learned and hand-designed optimizers. We further leverage our analysis to construct a learned optimizer that is both faster and more memory efficient than previous work. Our model and training code are open source.

The efficacy of large language models (LLMs) in understanding and generating natural language has aroused a wide interest in developing prompt-based methods to harness the power of black-box LLMs. Existing methodologies usually prioritize a global optimization for finding the global optimum, which however will perform poorly in certain tasks. This thus motivates us to re-think the necessity of finding a global optimum in prompt optimization. To answer this, we conduct a thorough empirical study on prompt optimization and draw two major insights. Contrasting with the rarity of global optimum, local optima are usually prevalent and well-performed, which can be more worthwhile for efficient prompt optimization (Insight I). The choice of the input domain, covering both the generation and the representation of prompts, affects the identification of well-performing local optima (Insight II). Inspired by these insights, we propose a novel algorithm, namely localized zeroth-order prompt optimization (ZOPO), which incorporates a Neural Tangent Kernel-based derived Gaussian process into standard zeroth-order optimization for an efficient search of well-performing local optima in prompt optimization. Remarkably, ZOPO outperforms existing baselines in terms of both the optimization performance and the query efficiency, which we demonstrate through extensive experiments.

The rapid development of large language model (LLM) alignment algorithms has resulted in a complex and fragmented landscape, with limited clarity on the effectiveness of different methods and their inter-connections. This paper introduces Reward-Aware Preference Optimization (RPO), a mathematical framework that unifies popular preference optimization techniques in LLM alignment, including DPO, IPO, SimPO, and REINFORCE (LOO), among others. RPO provides a structured approach to disentangle and systematically study the impact of various design choices, such as the optimization objective, the number of responses per prompt, and the use of implicit versus explicit reward models, on LLM preference optimization. We additionally propose a new experimental setup that enables the clean and direct ablation of such design choices. Through an extensive series of ablation studies within the RPO framework, we gain insights into the critical factors shaping model alignment, offering practical guidance on the most effective strategies for improving LLM alignment.

Intervention-based model steering offers a lightweight and interpretable alternative to prompting and fine-tuning. However, by adapting strong optimization objectives from fine-tuning, current methods are susceptible to overfitting and often underperform, sometimes generating unnatural outputs. We hypothesize that this is because effective steering requires the faithful identification of internal model mechanisms, not the enforcement of external preferences. To this end, we build on the principles of distributed alignment search (DAS), the standard for causal variable localization, to propose a new steering method: Concept DAS (CDAS). While we adopt the core mechanism of DAS, distributed interchange intervention (DII), we introduce a novel distribution matching objective tailored for the steering task by aligning intervened output distributions with counterfactual distributions. CDAS differs from prior work in two main ways: first, it learns interventions via weak-supervised distribution matching rather than probability maximization; second, it uses DIIs that naturally enable bi-directional steering and allow steering factors to be derived from data, reducing the effort required for hyperparameter tuning and resulting in more faithful and stable control. On AxBench, a large-scale model steering benchmark, we show that CDAS does not always outperform preference-optimization methods but may benefit more from increased model scale. In two safety-related case studies, overriding refusal behaviors of safety-aligned models and neutralizing a chain-of-thought backdoor, CDAS achieves systematic steering while maintaining general model utility. These results indicate that CDAS is complementary to preference-optimization approaches and conditionally constitutes a robust approach to intervention-based model steering. Our code is available at https://github.com/colored-dye/concept_das.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

This systematic review explores the application of Large Language Models (LLMs) in Combinatorial Optimization (CO). We report our findings using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. We conduct a literature search via Scopus and Google Scholar, examining over 2,000 publications. We assess publications against four inclusion and four exclusion criteria related to their language, research focus, publication year, and type. Eventually, we select 103 studies. We classify these studies into semantic categories and topics to provide a comprehensive overview of the field, including the tasks performed by LLMs, the architectures of LLMs, the existing datasets specifically designed for evaluating LLMs in CO, and the field of application. Finally, we identify future directions for leveraging LLMs in this field.

While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly generating valid plans for complex planning problems such as multi-constraint or long-horizon tasks. On the other hand, many frameworks aiming to solve complex planning problems often rely on task-specific preparatory efforts, such as task-specific in-context examples and pre-defined critics/verifiers, which limits their cross-task generalization capability. In this paper, we tackle these challenges by observing that the core of many planning problems lies in optimization problems: searching for the optimal solution (best plan) with goals subject to constraints (preconditions and effects of decisions). With LLMs' commonsense, reasoning, and programming capabilities, this opens up the possibilities of a universal LLM-based approach to planning problems. Inspired by this observation, we propose LLMFP, a general-purpose framework that leverages LLMs to capture key information from planning problems and formally formulate and solve them as optimization problems from scratch, with no task-specific examples needed. We apply LLMFP to 9 planning problems, ranging from multi-constraint decision making to multi-step planning problems, and demonstrate that LLMFP achieves on average 83.7% and 86.8% optimal rate across 9 tasks for GPT-4o and Claude 3.5 Sonnet, significantly outperforming the best baseline (direct planning with OpenAI o1-preview) with 37.6% and 40.7% improvements. We also validate components of LLMFP with ablation experiments and analyzed the underlying success and failure reasons.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

Can a single LLM-based optimization system match specialized tools across fundamentally different domains? We show that when optimization problems are formulated as improving a text artifact evaluated by a scoring function, a single AI-based optimization system-supporting single-task search, multi-task search with cross-problem transfer, and generalization to unseen inputs-achieves state-of-the-art results across six diverse tasks. Our system discovers agent architectures that nearly triple Gemini Flash's ARC-AGI accuracy (32.5% to 89.5%), finds scheduling algorithms that cut cloud costs by 40%, generates CUDA kernels where 87% match or beat PyTorch, and outperforms AlphaEvolve's reported circle packing solution (n=26). Ablations across three domains reveal that actionable side information yields faster convergence and substantially higher final scores than score-only feedback, and that multi-task search outperforms independent optimization given equivalent per-problem budget through cross-task transfer, with benefits scaling with the number of related tasks. Together, we show for the first time that text optimization with LLM-based search is a general-purpose problem-solving paradigm, unifying tasks traditionally requiring domain-specific algorithms under a single framework. We open-source optimize\_anything with support for multiple backends as part of the GEPA project at https://github.com/gepa-ai/gepa .

Most LLM-based automated algorithm design methods optimize a designated component within a human-specified scaffold, fixing overall organization and component interactions. We present ATLAS, an embedding-guided quality-diversity framework for scaffold-free full-algorithm synthesis in combinatorial optimization. The problem specification supplies objectives and constraints; a minimal I/O interface fixes only instance and solution formats; the LLM chooses and restructures components, interactions, and control flow. This freedom enlarges the search space, risking invalid candidates and premature convergence to one design region. ATLAS independently detects execution, interface, and feasibility failures, recomputes objectives, and applies error-conditioned repair; similarity-based archive management preserves algorithms across embedding-space regions to counter premature convergence. Its three-layer search refines the best design, gives other regions dedicated refinement opportunities, and performs cross-region synthesis to recombine components and their interactions. Across four NP-hard problems, ATLAS outperforms several state-of-the-art component-synthesis methods and a matched full-synthesis baseline while remaining competitive with strong human-designed algorithms. One ATLAS run retains several algorithms with comparable performance from distinct embedding-space regions rather than a single design. Code inspection finds that these multi-component designs differ in their primary construction or global-search backbone. Our results suggest that embedding-guided quality-diversity search can make the enlarged full-algorithm design space practically searchable. Source code and exact executable prompts are available at <https://github.com/Danial-Yazdani/ATLAS>.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

Augmenting large language models (LLMs) with external tools is a promising approach to enhance their capabilities. Effectively leveraging this potential for complex tasks hinges crucially on improving their ability to use tools. Synthesizing tool use data by simulating the real world is an effective approach. Nevertheless, our investigation reveals that training gains significantly decay as the scale of these data increases. The primary factor is the model's poor performance (a.k.a deficiency) in complex scenarios, which hinders learning from data using SFT. Driven by this objective, we propose an iterative reinforced fine-tuning strategy to continually guide the model to alleviate it. Specifically, we first identify deficiency-related data based on feedback from the policy model, then perform a Monte Carlo Tree Search to collect fine-grained preference pairs to pinpoint deficiencies. Subsequently, we update the policy model using preference optimization to align with ground truth and misalign with deficiencies. This process can be iterated. Moreover, before the iteration, we propose an easy-to-hard warm-up SFT strategy to facilitate learning from challenging data. The experiments demonstrate our models go beyond the same parametric models, outperforming many larger open-source and closed-source models. Additionally, it has achieved notable training gains in complex tool use scenarios.

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

Recent work has demonstrated the promise of orchestrating large language models (LLMs) within evolutionary and agentic optimization systems. However, the mechanisms driving these optimization gains remain poorly understood. In this work, we present a large-scale study of LLM-guided evolutionary search, collecting optimization trajectories for 15 LLMs across 8 tasks. Although zero-shot problem-solving ability correlates with final optimization outcomes, it explains only part of the variance: models with similar initial capability often induce dramatically different search trajectories and outcomes. By analyzing these trajectories, we find that strong LLM optimizers behave as local refiners, producing frequent incremental improvements while progressively localizing the search in semantic space. Conversely, weaker optimizers exhibit large semantic drift, with sporadic breakthroughs followed by stagnation. Notably, various measures of solution novelty do not predict final performance; novelty is beneficial only when the search remains sufficiently localized around high-performing regions of the solution space. Our results highlight the importance of trajectory analysis for understanding and improving LLM-based optimization systems and provide actionable insights for their design and training.

In this paper, we present NEMO, a system that translates Natural-language descriptions of decision problems into formal Executable Mathematical Optimization implementations, operating collaboratively with users or autonomously. Existing approaches typically rely on specialized large language models (LLMs) or bespoke, task-specific agents. Such methods are often brittle, complex and frequently generating syntactically invalid or non-executable code. NEMO instead centers on remote interaction with autonomous coding agents (ACAs), treated as a first-class abstraction analogous to API-based interaction with LLMs. This design enables the construction of higher-level systems around ACAs that structure, consolidate, and iteratively refine task specifications. Because ACAs execute within sandboxed environments, code produced by NEMO is executable by construction, allowing automated validation and repair. Building on this, we introduce novel coordination patterns with and across ACAs, including asymmetric validation loops between independently generated optimizer and simulator implementations (serving as a high-level validation mechanism), external memory for experience reuse, and robustness enhancements via minimum Bayes risk (MBR) decoding and self-consistency. We evaluate NEMO on nine established optimization benchmarks. As depicted in Figure 1, it achieves state-of-the-art performance on the majority of tasks, with substantial margins on several datasets, demonstrating the power of execution-aware agentic architectures for automated optimization modeling.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we develop an iterative approach that optimizes the preference between competing generated Chain-of-Thought (CoT) candidates by optimizing for winning vs. losing reasoning steps that lead to the correct answer. We train using a modified DPO loss (Rafailov et al., 2023) with an additional negative log-likelihood term, which we find to be crucial. We show reasoning improves across repeated iterations of this scheme. While only relying on examples in the training set, our approach results in increasing accuracy for Llama-2-70B-Chat from 55.6% to 81.6% on GSM8K (and 88.7% with majority voting out of 32 samples), from 12.5% to 20.8% on MATH, and from 77.8% to 86.7% on ARC-Challenge, which outperforms other Llama-2-based models not relying on additionally sourced datasets.

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

Bayesian optimization (BO) is a powerful approach for optimizing complex and expensive-to-evaluate black-box functions. Its importance is underscored in many applications, notably including hyperparameter tuning, but its efficacy depends on efficiently balancing exploration and exploitation. While there has been substantial progress in BO methods, striking this balance remains a delicate process. In this light, we present LLAMBO, a novel approach that integrates the capabilities of Large Language Models (LLM) within BO. At a high level, we frame the BO problem in natural language, enabling LLMs to iteratively propose and evaluate promising solutions conditioned on historical evaluations. More specifically, we explore how combining contextual understanding, few-shot learning proficiency, and domain knowledge of LLMs can improve model-based BO. Our findings illustrate that LLAMBO is effective at zero-shot warmstarting, and enhances surrogate modeling and candidate sampling, especially in the early stages of search when observations are sparse. Our approach is performed in context and does not require LLM finetuning. Additionally, it is modular by design, allowing individual components to be integrated into existing BO frameworks, or function cohesively as an end-to-end method. We empirically validate LLAMBO's efficacy on the problem of hyperparameter tuning, highlighting strong empirical performance across a range of diverse benchmarks, proprietary, and synthetic tasks.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in https://github.com/research4pan/Plum.

We ask whether large language models (LLMs) can design effective algorithms for well-specified operations research (OR) problems. We study inventory control, queueing network control, and assortment optimization, using benchmark instances from recent papers in each area. We evaluate two levels of LLM use: at level 1, the model receives one problem instance and returns a solution for that instance; at level 2, it receives only the problem class description and broad parameter ranges, and returns an algorithm that maps instance parameters to solutions. Human input is minimal: we give one untuned prompt that describes the problem, and the model has access to a Python sandbox tool with a fixed compute budget. The strongest model we test, gpt-5.6-sol, matches or outperforms the best method reported in those papers on almost all evaluated instances. This holds even at level 2, where the returned algorithm is fixed before seeing the evaluation instances. Performance also improves sharply across models released less than eight months apart, suggesting that this capability is moving quickly. Thus, for the well-specified operations problems we study, a single untuned LLM query can already produce algorithms competitive with specialized methods. These results suggest that frontier LLMs can be a serious empirical baseline for algorithm design in well-specified OR problems.

Optimizing complex systems, ranging from LLM prompts to multi-turn agents, traditionally requires labor-intensive manual iteration. We formalize this challenge as a stochastic generative optimization problem where a generative language model acts as the optimizer, guided by numerical rewards and text feedback to discover the best system. We introduce Prioritized Optimization with Local Contextual Aggregation (POLCA), a scalable framework designed to handle stochasticity in optimization -- such as noisy feedback, sampling minibatches, and stochastic system behaviors -- while effectively managing the unconstrained expansion of solution space. POLCA maintains a priority queue to manage the exploration-exploitation tradeoff, systematically tracking candidate solutions and their evaluation histories. To enhance efficiency, we integrate an varepsilon-Net mechanism to maintain parameter diversity and an LLM Summarizer to perform meta-learning across historical trials. We theoretically prove that POLCA converges to near-optimal candidate solutions under stochasticity. We evaluate our framework on diverse benchmarks, including τ-bench, HotpotQA (agent optimization), VeriBench (code translation) and KernelBench (CUDA kernel generation). Experimental results demonstrate that POLCA achieves robust, sample and time-efficient performance, consistently outperforming state-of-the-art algorithms in both deterministic and stochastic problems. The codebase for this work is publicly available at https://github.com/rlx-lab/POLCA.

Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph representation scheme is unsuitable for modelling partial solutions at each construction step. This paper proposes a novel DRL-guided improvement heuristic for solving JSSP, where graph representation is employed to encode complete solutions. We design a Graph Neural-Network-based representation scheme, consisting of two modules to effectively capture the information of dynamic topology and different types of nodes in graphs encountered during the improvement process. To speed up solution evaluation during improvement, we present a novel message-passing mechanism that can evaluate multiple solutions simultaneously. We prove that the computational complexity of our method scales linearly with problem size. Experiments on classic benchmarks show that the improvement policy learned by our method outperforms state-of-the-art DRL-based methods by a large margin.

Automated harness optimization can substantially improve LLM agents by iteratively updating their prompts, tool interfaces, and control logic from execution feedback. However, existing methods primarily optimize how the harness is updated while largely fixing which training scenarios generate the feedback that drives those updates. As the harness evolves, the scenarios most useful for further optimization can change, suggesting that the training curriculum itself should adapt alongside the harness. We formulate this missing dimension of harness optimization as an automated curriculum learning problem and introduce ActiveSaddler. ActiveSaddler models the evolving curriculum as a non-stationary bandit with dynamically instantiated optimization targets. It abstracts recurring failures into reusable failure-pattern arms, estimates the potential learning progress from further targeting each pattern, and adaptively balances revisiting known weaknesses with exploring unseen scenarios for new ones. Optimization outcomes continually update both the set of discovered failure patterns and their priorities, allowing the curriculum to co-evolve with the harness. Experiments on GAIA2 and Terminal-Bench 2.0 show that ActiveSaddler consistently discovers stronger harnesses, improving test Pass@1 by 4.4 and 7.5 percentage points over the same harness optimizer using a scenario order fixed before optimization, respectively. Ablations further show that these gains depend on dynamically constructing optimization targets, estimating their evolving utility, and balancing continued optimization with new failure discovery. Together, these results establish automated curriculum learning as a new crucial optimization dimension for harness optimization.

The Base-New Trade-off (BNT) problem universally exists during the optimization of CLIP-based prompt tuning, where continuous fine-tuning on base (target) classes leads to a simultaneous decrease of generalization ability on new (unseen) classes. Existing approaches attempt to regulate the prompt tuning process to balance BNT by appending constraints. However, imposed on the same target prompt, these constraints fail to fully avert the mutual exclusivity between the optimization directions for base and new. As a novel solution to this challenge, we propose the plug-and-play Dual-Prompt Collaboration (DPC) framework, the first that decoupling the optimization processes of base and new tasks at the prompt level. Specifically, we clone a learnable parallel prompt based on the backbone prompt, and introduce a variable Weighting-Decoupling framework to independently control the optimization directions of dual prompts specific to base or new tasks, thus avoiding the conflict in generalization. Meanwhile, we propose a Dynamic Hard Negative Optimizer, utilizing dual prompts to construct a more challenging optimization task on base classes for enhancement. For interpretability, we prove the feature channel invariance of the prompt vector during the optimization process, providing theoretical support for the Weighting-Decoupling of DPC. Extensive experiments on multiple backbones demonstrate that DPC can significantly improve base performance without introducing any external knowledge beyond the base classes, while maintaining generalization to new classes. Code is available at: https://github.com/JREion/DPC.

Alignment in artificial intelligence pursues the consistency between model responses and human preferences as well as values. In practice, the multifaceted nature of human preferences inadvertently introduces what is known as the "alignment tax" -a compromise where enhancements in alignment within one objective (e.g.,harmlessness) can diminish performance in others (e.g.,helpfulness). However, existing alignment techniques are mostly unidirectional, leading to suboptimal trade-offs and poor flexibility over various objectives. To navigate this challenge, we argue the prominence of grounding LLMs with evident preferences. We introduce controllable preference optimization (CPO), which explicitly specifies preference scores for different objectives, thereby guiding the model to generate responses that meet the requirements. Our experimental analysis reveals that the aligned models can provide responses that match various preferences among the "3H" (helpfulness, honesty, harmlessness) desiderata. Furthermore, by introducing diverse data and alignment goals, we surpass baseline methods in aligning with single objectives, hence mitigating the impact of the alignment tax and achieving improvements in multi-objective alignment.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

Automatic Prompt Optimization (APO) has emerged as a critical technique for enhancing Large Language Model (LLM) performance, yet current state-of-the-art methods typically rely on large, labeled gold-standard development sets to compute fitness scores for evolutionary or Reinforcement Learning (RL) approaches. In real-world software engineering, however, such curated datasets are rarely available during the initial cold start of agent development, where engineers instead face messy production logs and evolving failure modes. We present ROAD (Reflective Optimization via Automated Debugging), a novel framework that bypasses the need for refined datasets by treating optimization as a dynamic debugging investigation rather than a stochastic search. Unlike traditional mutation strategies, ROAD utilizes a specialized multi-agent architecture, comprising an Analyzer for root-cause analysis, an Optimizer for pattern aggregation, and a Coach for strategy integration, to convert unstructured failure logs into robust, structured Decision Tree Protocols. We evaluated ROAD across both a standardized academic benchmark and a live production Knowledge Management engine. Experimental results demonstrate that ROAD is highly sample-efficient, achieving a 5.6 percent increase in success rate (73.6 percent to 79.2 percent) and a 3.8 percent increase in search accuracy within just three automated iterations. Furthermore, on complex reasoning tasks in the retail domain, ROAD improved agent performance by approximately 19 percent relative to the baseline. These findings suggest that mimicking the human engineering loop of failure analysis and patching offers a viable, data-efficient alternative to resource-intensive RL training for deploying reliable LLM agents.

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly 2% of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the k-adaptability algorithm, particularly on the largest instances, with a 10 to 100-fold reduction in solution time. Our code and data are available at https://github.com/khalil-research/Neur2RO.

Learned optimization has emerged as a promising alternative to hand-crafted optimizers, with the potential to discover stronger learned update rules that enable faster, hyperparameter-free training of neural networks. A critical element for practically useful learned optimizers, that can be used off-the-shelf after meta-training, is strong meta-generalization: the ability to apply the optimizers to new tasks. Recent state-of-the-art work in learned optimizers, VeLO (Metz et al., 2022), requires a large number of highly diverse meta-training tasks along with massive computational resources, 4000 TPU months, to achieve meta-generalization. This makes further improvements to such learned optimizers impractical. In this work, we identify several key elements in learned optimizer architectures and meta-training procedures that can lead to strong meta-generalization. We also propose evaluation metrics to reliably assess quantitative performance of an optimizer at scale on a set of evaluation tasks. Our proposed approach, Celo, makes a significant leap in improving the meta-generalization performance of learned optimizers and also outperforms tuned state-of-the-art optimizers on a diverse set of out-of-distribution tasks, despite being meta-trained for just 24 GPU hours.

Leveraging Large Language Models (LLMs) to automatically formulate and solve optimization problems from natural language has emerged as an efficient paradigm for automated optimization. However, existing methods still exhibit limited generalization: they are sensitive to superficial narrative variations, reuse experience mainly at the case level, and struggle to adapt to shifted or emerging problem types. We propose OptSkills, an archetype-centric skill learning and reasoning agent system for optimization modeling and solving. To improve robust generalization, our system clusters problems by their underlying archetypes rather than surface narratives. To improve in-distribution generalization, it explores diverse modeling paradigms and solver configurations within each cluster, then distills successful trajectories into reusable workflow-level skills. To improve out-of-distribution generalization, it refines existing skills or expands the skill library using newly obtained trajectories. Our system achieves a state-of-the-art micro-averaged accuracy of 68.27% on datasets encompassing diverse problem types and scenarios. In addition, on MIPLIB-NL, a highly challenging large-scale and high-dimensional benchmark, it achieves 26.91% accuracy, outperforming DeepSeek-V3.2-Thinking by 4.53%. After skill learning on Nano-CO, it reaches 72.79% on the OOD NLCO benchmark. Code and skills are available at https://github.com/fujiwaranoM0kou/OptSkills.

Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on a few number of objectives and cannot scale to many objectives that outnumber the solutions, leading to either subpar performance or ignored objectives. We introduce Many-objective multi-solution Transport (MosT), a framework that finds multiple diverse solutions in the Pareto front of many objectives. Our insight is to seek multiple solutions, each performing as a domain expert and focusing on a specific subset of objectives while collectively covering all of them. MosT formulates the problem as a bi-level optimization of weighted objectives for each solution, where the weights are defined by an optimal transport between the objectives and solutions. Our algorithm ensures convergence to Pareto stationary solutions for complementary subsets of objectives. On a range of applications in federated learning, multi-task learning, and mixture-of-prompt learning for LLMs, MosT distinctly outperforms strong baselines, delivering high-quality, diverse solutions that profile the entire Pareto frontier, thus ensuring balanced trade-offs across many objectives.

Reinforcement Learning (RL) has emerged as a powerful tool for neural combinatorial optimization, enabling models to learn heuristics that solve complex problems without requiring expert knowledge. Despite significant progress, existing RL approaches face challenges such as diminishing reward signals and inefficient exploration in vast combinatorial action spaces, leading to inefficiency. In this paper, we propose Preference Optimization, a novel method that transforms quantitative reward signals into qualitative preference signals via statistical comparison modeling, emphasizing the superiority among sampled solutions. Methodologically, by reparameterizing the reward function in terms of policy and utilizing preference models, we formulate an entropy-regularized RL objective that aligns the policy directly with preferences while avoiding intractable computations. Furthermore, we integrate local search techniques into the fine-tuning rather than post-processing to generate high-quality preference pairs, helping the policy escape local optima. Empirical results on various benchmarks, such as the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP) and the Flexible Flow Shop Problem (FFSP), demonstrate that our method significantly outperforms existing RL algorithms, achieving superior convergence efficiency and solution quality.

Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE\_code.

Global optimization of expensive, derivative-free black-box functions demands extreme sample efficiency and decision interpretability. While Large Language Models (LLMs) have shown broad capabilities, even state-of-the-art models remain limited in solving continuous black-box optimization tasks and struggle to maintain exploration-exploitation balance. We introduce GPTOpt, an optimization method that equips LLMs with continuous black-box optimization capabilities by fine-tuning Llama 3.1 8B on structured Bayesian optimization (BO) data, including surrogate model information. This provides an explainable framework calibrated to produce surrogate model outputs comparable to a Gaussian process, while keeping the advantages of flexible LLM-based optimization. On a variety of black-box optimization benchmarks, our model shows favorable performance compared to traditional optimizers and transformer-based alternatives, while providing important context and insight into the model's decisions.

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods.

Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in accelerating MILP solvers by predicting high-quality solutions. However, we identify that existing methods misalign with the intrinsic structure of MILP problems at two levels. At the leaning objective level, the Binary Cross-Entropy (BCE) loss treats variables independently, neglecting their relative priority and yielding plausible logits. At the model architecture level, standard GNN message passing inherently smooths the representations across variables, missing the natural competitive relationships within constraints. To address these challenges, we propose CoCo-MILP, which explicitly models inter-variable Contrast and intra-constraint Competition for advanced MILP solution prediction. At the objective level, CoCo-MILP introduces the Inter-Variable Contrastive Loss (VCL), which explicitly maximizes the embedding margin between variables assigned one versus zero. At the architectural level, we design an Intra-Constraint Competitive GNN layer that, instead of homogenizing features, learns to differentiate representations of competing variables within a constraint, capturing their exclusionary nature. Experimental results on standard benchmarks demonstrate that CoCo-MILP significantly outperforms existing learning-based approaches, reducing the solution gap by up to 68.12% compared to traditional solvers. Our code is available at https://github.com/happypu326/CoCo-MILP.

Learning to optimize has emerged as a powerful framework for various optimization and machine learning tasks. Current such "meta-optimizers" often learn in the space of continuous optimization algorithms that are point-based and uncertainty-unaware. To overcome the limitations, we propose a meta-optimizer that learns in the algorithmic space of both point-based and population-based optimization algorithms. The meta-optimizer targets at a meta-loss function consisting of both cumulative regret and entropy. Specifically, we learn and interpret the update formula through a population of LSTMs embedded with sample- and feature-level attentions. Meanwhile, we estimate the posterior directly over the global optimum and use an uncertainty measure to help guide the learning process. Empirical results over non-convex test functions and the protein-docking application demonstrate that this new meta-optimizer outperforms existing competitors.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC optimizer. These constructed optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings.

Enterprise LLM deployment faces a critical scalability challenge: organizations must optimize models systematically to scale AI initiatives within constrained compute budgets, yet the specialized expertise required for manual optimization remains a niche and scarce skillset. This challenge is particularly evident in managing GPU utilization across heterogeneous infrastructure while enabling teams with diverse workloads and limited LLM optimization experience to deploy models efficiently. We present OptiKIT, a distributed LLM optimization framework that democratizes model compression and tuning by automating complex optimization workflows for non-expert teams. OptiKIT provides dynamic resource allocation, staged pipeline execution with automatic cleanup, and seamless enterprise integration. In production, it delivers more than 2x GPU throughput improvement while empowering application teams to achieve consistent performance improvements without deep LLM optimization expertise. We share both the platform design and key engineering insights into resource allocation algorithms, pipeline orchestration, and integration patterns that enable large-scale, production-grade democratization of model optimization. Finally, we open-source the system to enable external contributions and broader reproducibility.

Well-designed prompts are crucial for enhancing Large language models' (LLMs) reasoning capabilities while aligning their outputs with task requirements across diverse domains. However, manually designed prompts require expertise and iterative experimentation. While existing prompt optimization methods aim to automate this process, they rely heavily on external references such as ground truth or by humans, limiting their applicability in real-world scenarios where such data is unavailable or costly to obtain. To address this, we propose Self-Supervised Prompt Optimization (SPO), a cost-efficient framework that discovers effective prompts for both closed and open-ended tasks without requiring external reference. Motivated by the observations that prompt quality manifests directly in LLM outputs and LLMs can effectively assess adherence to task requirements, we derive evaluation and optimization signals purely from output comparisons. Specifically, SPO selects superior prompts through pairwise output comparisons evaluated by an LLM evaluator, followed by an LLM optimizer that aligns outputs with task requirements. Extensive experiments demonstrate that SPO outperforms state-of-the-art prompt optimization methods, achieving comparable or superior results with significantly lower costs (e.g., 1.1% to 5.6% of existing methods) and fewer samples (e.g., three samples). The code is available at https://github.com/geekan/MetaGPT.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

The rise of foundation models has shifted focus from resource-intensive fine-tuning to prompt engineering, a paradigm that steers model behavior through input design rather than weight updates. While manual prompt engineering faces limitations in scalability, adaptability, and cross-modal alignment, automated methods, spanning foundation model (FM) based optimization, evolutionary methods, gradient-based optimization, and reinforcement learning, offer promising solutions. Existing surveys, however, remain fragmented across modalities and methodologies. This paper presents the first comprehensive survey on automated prompt engineering through a unified optimization-theoretic lens. We formalize prompt optimization as a maximization problem over discrete, continuous, and hybrid prompt spaces, systematically organizing methods by their optimization variables (instructions, soft prompts, exemplars), task-specific objectives, and computational frameworks. By bridging theoretical formulation with practical implementations across text, vision, and multimodal domains, this survey establishes a foundational framework for both researchers and practitioners, while highlighting underexplored frontiers in constrained optimization and agent-oriented prompt design.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

While accelerated computing has transformed many domains of computing, its impact on logical reasoning, specifically Boolean satisfiability (SAT), remains limited. State-of-the-art SAT solvers rely heavily on inherently sequential conflict-driven search algorithms that offer powerful heuristics but limit the amount of parallelism that could otherwise enable significantly more scalable SAT solving. Inspired by neural network training, we formulate the SAT problem as a binarized matrix-matrix multiplication layer that could be optimized using a differentiable objective function. Enabled by this encoding, we combine the strengths of parallel differentiable optimization and sequential search to accelerate SAT on a hybrid GPU-CPU system. In this system, the GPUs leverage parallel differentiable solving to rapidly evaluate SAT clauses and use gradients to stochastically explore the solution space and optimize variable assignments. Promising partial assignments generated by the GPUs are post-processed on many CPU threads which exploit conflict-driven sequential search to further traverse the solution subspaces and identify complete assignments. Prototyping the hybrid solver on an NVIDIA DGX GB200 node, our solver achieves runtime speedups up to over 200x when compared to a state-of-the-art CPU-based solver on public satisfiable benchmark problems from the SAT Competition.