Learning to Optimize

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5 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

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Latest papers 83

Apr 29, 2026math.OC

Learning Over-Relaxation Policies for ADMM with Convergence Guarantees

The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such as Model Predictive Control (MPC), where one repeatedly solves related optimization problems with fixed structure and changing parameter values, we propose learning online updates of the relaxation parameter to improve average performance on problem classes of interest, while guaranteeing that asymptotic convergence is not compromised for the worst-case realization of such problems. This choice is computationally attractive in the Operator Splitting Quadratic Program (OSQP)-like architectures, since adapting relaxation does not trigger the matrix refactorizations associated with penalty updates. We establish convergence guarantees for ADMM with time-varying penalty and relaxation parameters under mild assumptions, and show on benchmark quadratic programs that the resulting learned policies improve both iteration count and wall-clock time on average over baseline OSQP.

Junan Lin, Paul J. Goulart, Luca Furieri

Department of Engineering Science, University of Oxford, OX1 3PJ Oxford, UK

Learning to Optimize Alternating Direction Method of Multipliers Constrained Optimization

Apr 28, 2026math.OC

Accelerating Regularized Attention Kernel Regression for Spectrum Cartography

Spectrum cartography reconstructs spatial radio fields from sparse and heterogeneous wireless measurements, underpinning many sensing and optimization tasks in wireless networks. Attention mechanisms have recently enabled adaptive measurement aggregation via attention kernel-based formulations. However, the resulting exponential kernels exhibit severe spectral imbalance, inducing large condition numbers that render standard iterative solvers ineffective for regularized attention kernel regression. This paper proposes a Learning-based Attention Kernel Regression (LAKER) algorithm for accelerating regularized attention kernel regression in spectrum cartography. The key idea is to learn a data-dependent preconditioner that captures the inverse spectral structure of the attention kernel system, directly reducing the condition number bottleneck. The preconditioner is obtained by solving a regularized maximum-likelihood estimation problem via a shrinkage-regularized convex--concave procedure, and is integrated with a preconditioned conjugate gradient solver for efficient optimization, whose solution is used for radio map reconstruction. Extensive experiments demonstrate that LAKER significantly reduces condition numbers by up to three orders of magnitude, accelerates convergence by over twenty-fold compared to baselines, and maintains high reconstruction accuracy, establishing learning-based preconditioning as an effective approach for attention kernel regression in spectrum cartography.

Liping Tao, Chee Wei Tan

College of Computing and Data Science, Nanyang Technological University, Singapore 639798

Learning to Optimize

Apr 23, 2026cs.LG

Transferable SCF-Acceleration through Solver-Aligned Initialization Learning

The cost of Kohn-Sham density functional theory (KS-DFT) calculations scales with the number of solver iterations, which depends on the quality of the initial guess. Machine learning methods that predict initial guesses from molecular geometry can reduce this cost, but matrix-prediction models fail when extrapolating to larger molecules, degrading rather than accelerating convergence [Liu et al., 2025]. We show that this failure is a supervision problem, not an extrapolation problem: models trained on ground-state targets fit those targets well out of distribution, yet produce initial guesses that slow convergence. Solver-Aligned Initialization Learning (SAIL) resolves this for both Hamiltonian and density matrix models by differentiating through the self-consistent field (SCF) solver end-to-end. We introduce the Effective Relative Iteration Count (ERIC), a correction to the commonly used RIC that accounts for hidden Fock-build overhead. On QM40, which contains molecules up to 4

\times

larger than the training distribution, SAIL reduces ERIC by 37% (PBE), 33% (SCAN), and 28% (B3LYP), more than doubling the previous state-of-the-art reduction on B3LYP. On QMugs molecules 10

\times

larger than the training set, SAIL delivers a 1.35

\times

wall-time speedup at the hybrid level of theory, extending ML SCF acceleration to large drug-like molecules.

Eike S. Eberhard, Viktor Kotsev, Timm Güthle +1

1Technical University of Munich (TUM) · 2Munich Data Science Institute (MDSI) · 3Munich Center for Machine Learning (MCML)

Quantum Chemistry Learning to Optimize Scientific ML Computational Materials Science

Apr 22, 2026cs.AI

Learning to Evolve: A Self-Improving Framework for Multi-Agent Systems via Textual Parameter Graph Optimization

Designing and optimizing multi-agent systems (MAS) is a complex, labor-intensive process of "Agent Engineering." Existing automatic optimization methods, primarily focused on flat prompt tuning, lack the structural awareness to debug the intricate web of interactions in MAS. More critically, these optimizers are static; they do not learn from experience to improve their own optimization strategies. To address these gaps, we introduce Textual Parameter Graph Optimization (TPGO), a framework that enables a multi-agent system to learn to evolve. TPGO first models the MAS as a Textual Parameter Graph (TPG), where agents, tools, and workflows are modular, optimizable nodes. To guide evolution, we derive "textual gradients," structured natural language feedback from execution traces, to pinpoint failures and suggest granular modifications. The core of our framework is Group Relative Agent Optimization (GRAO), a novel meta-learning strategy that learns from historical optimization experiences. By analyzing past successes and failures, GRAO becomes progressively better at proposing effective updates, allowing the system to learn how to optimize itself. Extensive experiments on complex benchmarks like GAIA and MCP-Universe show that TPGO significantly enhances the performance of state-of-the-art agent frameworks, achieving higher success rates through automated, self-improving optimization.

Shan He, Runze Wang, Zhuoyun Du +4

Future Living Lab of Alibaba

Multi-Agent System Optimization Learning to Optimize Multi-Agent Systems Self-Improving Agents

Apr 21, 2026math.OC

Decision-Focused Federated Learning Under Heterogeneous Objectives and Constraints

We consider Decision-Focused Federated Learning (DFFL), a predict-then-optimize setting in which multiple clients collaboratively train predictive models for downstream linear optimization problems without exchanging raw data. Besides the data heterogeneity typical of standard federated learning, clients may also have different objective functions and feasible regions. Building on the SPO+ surrogate loss, we derive heterogeneity bounds that separate objective shift, measured through cost-vector distances, from feasible-set shift, measured through support-function and shape-distance terms. We show that, for general compact feasible sets, small objective perturbations can still induce nonvanishing decision-focused loss discrepancies, while strongly convex feasible regions yield sharper stability-based bounds. We then lift these pointwise bounds to a local-versus-federated excess-risk comparison, showing that federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty. Computational experiments on polyhedral and strongly convex problems confirm that federation is substantially more robust under strongly convex feasible regions. Finally, we evaluate a simple validation-based interpolation between local and federated DFFL models. This interpolation mitigates the theoretical tradeoff and reduces aggregate regret and worst-client harm in both synthetic experiments and a PJM energy-pricing case study.

Konstantinos Ziliaskopoulos, Alexander Vinel

Auburn University

Predict-Then-Optimize Learning to Optimize Decision-Focused Learning Constrained Optimization Federated Learning Heterogeneous Federated Learning

Apr 16, 2026cs.DB

RELOAD: A Robust and Efficient Learned Query Optimizer for Database Systems

Recent advances in query optimization have shifted from traditional rule-based and cost-based techniques towards machine learning-driven approaches. Among these, reinforcement learning (RL) has attracted significant attention due to its ability to optimize long-term performance by learning policies over query planning. However, existing RL-based query optimizers often exhibit unstable performance at the level of individual queries, including severe performance regressions, and require prolonged training to reach the plan quality of expert, cost-based optimizers. These shortcomings make learned query optimizers difficult to deploy in practice and remain a major barrier to their adoption in production database systems. To address these challenges, we present RELOAD, a robust and efficient learned query optimizer for database systems. RELOAD focuses on (i) robustness, by minimizing query-level performance regressions and ensuring consistent optimization behavior across executions, and (ii) efficiency, by accelerating convergence to expert-level plan quality. Through extensive experiments on standard benchmarks, including Join Order Benchmark, TPC-DS, and Star Schema Benchmark, RELOAD demonstrates up to 2.4x higher robustness and 3.1x greater efficiency compared to state-of-the-art RL-based query optimization techniques.

Seokwon Lee, Jaeyoung Sim, Sihyun Kim +3

Yonsei University BDAI Lab, Seoul 03722, South Korea · Microsoft Gray Systems Lab, Redmond, USA

Learning to Optimize Robust RL Relational Databases

Apr 14, 2026math.OC

HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization

This paper presents HUANet, a constrained deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable neural network for accelerating parametric constrained convex optimization. Existing end-to-end learning methods operate as black-box mappings from parameters to solutions, often without explicitly incorporating optimality principles or guaranteeing constraint satisfaction. To address these limitations, HUANet embeds a hard-constrained neural network within each unrolled ADMM iteration, where a differentiable correction stage enforces the affine equalities of the primal subproblem. Furthermore, we incorporate first-order optimality conditions into a self-supervised training loss to promote the convergence of the proposed unrolled algorithm. Extensive numerical experiments for benchmark optimization problems and a control application demonstrate and validate the effectiveness of HUANet in accelerating constrained convex optimization solving.

Trinh Tran, Binh Nguyen, Truong X. Nghiem

Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA

Learning to Optimize Alternating Direction Method of Multipliers Algorithm Unrolling Constrained Optimization

Apr 13, 2026math.OC

Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management science (OR/MS), which has long provided methodological foundations for sequential decision making under uncertainty. At the same time, deep learning advances, including feedforward neural networks, recurrent architectures, transformers, large language models (LLMs), and deep reinforcement learning, have expanded data-driven modeling for large-scale decisions. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision making under uncertainty, bridging neural architectures and OR/MS approaches to decision making. Its premise: deep learning complements optimization rather than replacing it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the mathematical rigor to represent constraints, recourse, uncertainty, and decision quality. The tutorial reviews key decision making foundations, connects them to the major neural architectures in modern AI, and organizes the field around three central themes: predict-then-optimize and decision-aware learning, learning-based decision generation under constraints for continuous and discrete problems with temporal coupling, and deep reinforcement learning for sequential and combinatorial decision making. Impact spans supply chains, service systems, healthcare and epidemic response, agriculture, energy, environmental sustainability, and autonomous operations. This tutorial frames these developments as part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS's role in shaping the next generation of integrated learning--optimization systems.

I. Esra Buyuktahtakin

Grado Department of Industrial and Systems Engineering, Virginia Tech Blacksburg, VA 24061, USA

Reinforcement Learning Predict-Then-Optimize Sequential Decision Making Learning to Optimize Decision-Focused Learning Decision-Making under Uncertainty

Apr 4, 2026cs.LG

One-Shot Localisation of the Global Minimum of a Noisy One-Dimensional Function: An Iterative Neural Minimizer Compared with Set Transformers and Classical Estimators

We study a passive form of global optimisation: from twenty noisy samples of an unknown one-dimensional function, predict where its global minimum lies, with no further queries. We introduce the Neural Function Minimizer (NFM), an iterative model that walks a position across the domain and, at every step, reads the samples near that position and attends to all twenty of them, and we compare it with two Set Transformers of the same size trained on the same data, one that answers with a single point and one that answers with a mixture of candidate locations, and with classical zero-query estimators, over three training seeds per learned model. On held-out cases from the training families the three learned models are tied on location error, and each is more accurate on average than every classical estimator; against the Gaussian-process posterior argmin the NFM's error is lower by 1.3 points of the domain. The NFM has lower regret than the single-point Set Transformer, and its per-case uncertainty has a better likelihood than that model's and orders the cases by error better than the mixture model's. The Gaussian process and the mixture model have lower regret, and on functions outside the training families the Gaussian process is the most accurate estimator. Where two valleys are equally deep, the form of an estimator's answer, not its architecture, decides whether it commits to a valley or answers between them: every estimator that returns one point fitted to distance, learned or spline-based, hedges in a fifth to nearly a third of exact ties, while estimators that name a mode commit, and one Gaussian-process posterior does both, depending on whether it is summarised by its median or its mode. We will release the benchmark and a self-checking harness; its cases are identical on different machines and its results agree to rounding.

Qusay Muzaffar, David Levin, Michael Werman

Department of Computer Science, The Hebrew University of Jerusalem, Israel · Department of Applied Mathematics, Tel Aviv University, Israel

Black-Box Optimization Zeroth-Order Optimization Learning to Optimize Global Optimization

Apr 2, 2026math.OC

When does learning pay off? A study on DRL-based dynamic algorithm configuration for carbon-aware scheduling

Deep reinforcement learning (DRL) has recently emerged as a promising tool for Dynamic Algorithm Configuration (DAC), enabling evolutionary algorithms to adapt their parameters online rather than relying on static tuned configurations. While DRL can learn effective control policies, training is computationally expensive. This cost may be justified if learned policies generalize, allowing the training effort to transfer across instance types and problem scales. Yet, for real-world optimization problems, it remains unclear whether this promise holds in practice and under which conditions the investment in learning pays off. In this work, we investigate this question in the context of the carbon-aware permutation flow-shop scheduling problem. We develop a DRL-based DAC framework and train it exclusively on small, simple instances. We then deploy the learned policy on both similar and more complex unseen instances and compare its performance against a static tuned baseline, which provides a fair point of comparison. Our findings show that the proposed method provides a strong dynamic algorithm control policy that can be effectively transferred to different unseen problem instances. Notably, on simple and cheap to compute instances, similar to those observed during training and tuning, DRL performs comparably with the statically tuned baseline. However, as instance characteristics diverge and computational complexities increase, the DRL-learned policy continuously outperforms static tuning. These results confirm that DRL can acquire robust and generalizable control policies which are effective beyond the training instance distributions. This ability to generalize across instance types makes the initial computational investment worthwhile, particularly in settings where static tuning struggles to adapt to changing problem scenarios.

Andrea Mencaroni, Robbert Reijnen, Yingqian Zhang +1

Department of Industrial Systems Engineering and Product Design, Ghent University, Ghent, Belgium · Industrial Systems Engineering (ISyE), Flanders Make, Kortrijk, Belgium · Eindhoven Artificial Intelligence Systems Institute, Eindhoven University of Technology, The Netherlands +1

RL Control Learning to Optimize Combinatorial Optimization

Feb 10, 2026cs.LG

Learning to Discover Iterative Spectral Algorithms

We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral information (e.g., eigenvalue estimates and residual norms), and predict recurrence coefficients for computing or applying a matrix polynomial tailored to a downstream task. The effectiveness of AutoSpec relies on three ingredients: an architecture whose inference pass implements short, executable numerical linear algebra recurrences; efficient training on small synthetic problems with transfer to large-scale real-world operators; and task-defined objectives that enforce the desired approximation or preconditioning behavior across the range of spectral profiles represented in the training set. We apply AutoSpec to discovering algorithms for representative tasks on spd matrices: accelerating matrix function approximation; accelerating sparse linear solvers; and spectral filtering/preconditioning for eigenvalue computations. On real-world matrices, the learned procedures deliver up to order-of-magnitude improvements in accuracy and/or reductions in iteration count, relative to spectrum-agnostic baselines. We find clear connections to classical theory: the induced polynomials may exhibit equioscillation behavior characteristic of Chebyshev polynomial approximation. The code is available at: https://github.com/zihanghliu/AutoSpec .

Zihang Liu, Oleg Balabanov, Yaoqing Yang +1

1International Computer Science Institute · University of California, Berkeley · 4Lawrence Berkeley National Laboratory +1

Automated Algorithm Discovery Learning to Optimize Spectral Methods

Jan 31, 2026cs.NE

Meta-Learning-Assisted Constraint Relaxation for Constrained Black-Box Optimization

Constraint handling is central to constrained black-box optimization (BBO), where objective improvement and feasibility restoration often provide conflicting search signals. Existing

ε

-relaxation methods are simple and effective, but their relaxation schedules are usually fixed or manually designed for a limited range of problems. To address this limitation, this letter proposes MeCO, a meta-learning-assisted optimizer that learns an adaptive

ε

-relaxation policy for constrained BBO. MeCO couples a SHADE optimizer with a Double Deep Q-Network controller. At each optimization step, the controller observes compact population and constraint features and selects a scalar action, which is decoded into a relaxation vector for the candidate comparison rule. The policy is trained across constrained BBO instances and then deployed on held-out problems without problem-specific tuning. Experiments on the CEC2017 constrained benchmark, 16 UAV path-planning tasks and eight real-world engineering problems provide evidence that MeCO transfers across held-out benchmark functions, higher dimensions, and an application-domain setting. Ablation and behavior analyses further clarify the roles of constraint-related state features, action scaling, reward shaping, and meta-training.

Sijie Ma, Zeyuan Ma, Yue-Jiao Gong +1

Hong Kong Polytechnic University · South China Normal University · South China University of Technology

Black-Box Optimization Learning to Optimize Constrained Optimization Derivative-Free Optimization

Jan 23, 2026cs.MS

Learning to Optimize by Differentiable Programming

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn how to design them. Modern frameworks such as PyTorch, TensorFlow, and JAX enable this paradigm through efficient automatic differentiation. Embedding first-order methods within these systems allows end-to-end training that improves convergence and solution quality. Guided by Fenchel-Rockafellar duality, the tutorial demonstrates how duality-informed iterative schemes such as the alternating direction method of multipliers, and the primal-dual hybrid gradient can be learned and adapted through representative case studies.

Liping Tao, Xindi Tong, Chee Wei Tan

Nanyang Technological University, Singapore · Nanyang Technological University, Singapore, Singapore

Primal-Dual Optimization Learning to Optimize Alternating Direction Method of Multipliers Differentiable Programming Constrained Optimization Differentiable Optimization

Nov 25, 2025eess.SY

Reinforcement Learning to Initialize Newton-Raphson for AC Power Flow with Quantum Annealing-Based Environment Updates

The Newton-Raphson (NR) method is widely used for solving power flow (PF) equations due to its quadratic convergence. However, its performance deteriorates under poor initialization or extreme operating scenarios, e.g., high levels of renewable energy penetration. We propose the use of reinforcement learning (RL) to optimize the initialization of NR, and introduce a quantum-enhanced RL environment update mechanism that addresses the combinatorially large action space at each RL timestep by formulating the voltage adjustment task as a Quadratic Unconstrained Binary Optimization (QUBO) problem, solved with an Ising machine. RL initialization is benchmarked against flat start and start from the DC (linearized) PF solution on a standard 4-bus system, Iwamoto's ill-conditioned 11-bus system, and the IEEE 118-bus system under normal and stressed loading and reactive power limits, with verified operational solutions. On all systems, a supervised initializer refined by RL requires fewer NR iterations than flat and DC starts and than the same initializer without RL, for all seeds. For example, on the 118-bus system under normal and stressed loading, it reached 2.04 and 2.86 NR iterations, compared with 3.02 and 5.13 from DC start and 2.61 and 3.09 without RL. In wall-clock time, this pays off only for an initializer integrated into the solver and reused for many solves on a fixed topology. On the 4-bus system, a quantum-enhanced RL agent with a quantum-inspired annealer moved challenging initial states that required 29 and 44 NR iterations to initializations that required three NR iterations within one RL timestep.

Zeynab Kaseb, Matthias Moller, Lindsay Spoor +4

Electrical Sustainable Energy, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands. · Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands. · Leiden Institute of Advanced Computer Science, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands. +3

Reinforcement Learning Quantum Annealing Learning to Optimize Power Systems

Oct 29, 2025cs.LG

Machine Learning Guided Optimal Transmission Switching to Mitigate Wildfire Ignition Risk

To mitigate acute wildfire ignition risks, utilities de-energize power lines in high-risk areas. The Optimal Power Shutoff (OPS) problem optimizes line energization statuses to manage wildfire ignition risks through de-energizations while reducing load shedding. OPS problems are computationally challenging Mixed-Integer Linear Programs (MILPs) that must be solved rapidly and frequently in operational settings. For a particular power system, OPS instances share a common structure with varying parameters related to wildfire risks, loads, and renewable generation. This motivates the use of Machine Learning (ML) for solving OPS problems by exploiting shared patterns across instances. In this paper, we develop an ML-guided framework that quickly produces high-quality de-energization decisions by extending existing ML-guided MILP solution methods while integrating domain knowledge on the number of energized and de-energized lines. Results on a large-scale realistic California-based synthetic test system show that the proposed ML-guided method produces high-quality solutions faster than traditional optimization methods.

Weimin Huang, Ryan Piansky, Bistra Dilkina +1

Department of Computer Science University of Southern California Los Angeles, CA, USA · School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA, USA

Mixed-Integer Linear Programming Learning to Optimize Power Systems

Oct 6, 2025math.OC

Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions

Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety of domains, including power systems and scheduling. However, to the best of our knowledge, existing data-driven inverse optimization methods primarily focus on learning objective functions under known constraints, and learning both objective functions and constraints from data for MILPs remains largely unexplored. In this paper, we propose a two-stage approach for a class of inverse optimization problems in which the objective is a linear combination of given feature functions and the constraints are parameterized by unknown functions and thresholds. Our method first learns the constraints and then, conditioned on the learned constraints, estimates the objective-function weights. On the theoretical side, we provide finite-sample guarantees for solving the proposed inverse optimization problem. To this end, we develop statistical learning tools for pseudo-metric spaces under sub-Gaussian assumptions and use them to derive a learning-theoretic framework for inverse optimization with both unknown objectives and constraints. On the experimental side, we demonstrate that our method successfully solves inverse optimization problems on scheduling instances formulated as ILPs with up to 100 decision variables.

Akira Kitaoka

Mixed-Integer Linear Programming Learning to Optimize Inverse Problems Integer Linear Programming

Aug 17, 2025cs.LG

L-SR1: Learned Symmetric-Rank-One Preconditioning

End-to-end deep learning has achieved impressive results but often relies on large labeled datasets, exhibits limited generalization to unseen scenarios, and incurs substantial computational cost. Classical optimization methods, in contrast, are more data-efficient and lightweight but frequently suffer from slow convergence. Learned optimizers aim to bridge this gap, yet existing approaches have focused primarily on first-order methods, while learned second-order optimization has received much less attention. We introduce L-SR1, a learned second-order optimizer inspired by the classical Symmetric Rank-One (SR1) method. At its core, L-SR1 employs a Projection-Guided Secant Mechanism (PGSM) that generates positive semi-definite preconditioners and biases meta-training toward the quasi-Newton secant relation. Through controlled analytic benchmarks, we study stability, generalization across problem dimensions, and search direction quality, and further evaluate L-SR1 on Monocular Human Mesh Recovery (HMR), where it outperforms both classical and learned optimization-based baselines. With a compact model and no reliance on task-specific fine-tuning or annotated data, L-SR1 demonstrates strong generalization and can be integrated into a broad range of iterative optimization problems to accelerate convergence and reduce the required number of iterations.

Gal Lifshitz, Shahar Zuler, Ori Fouks +1

Tel Aviv University, Tel Aviv, Israel.

Learning to Optimize Second-Order Optimization Quasi-Newton Methods

Jul 9, 2025cs.LG

Direct Regret Optimization in Bayesian Optimization

Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate hand-crafted acquisition functions and surrogate models for the underlying function, and often operate in a myopic manner. In this paper, we propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition by distilling from a set of candidate models and acquisitions, and explicitly targets minimizing the multi-step regret. Our framework leverages an ensemble of Gaussian Processes (GPs) with varying hyperparameters to generate simulated BO trajectories, each guided by an acquisition function drawn from a pool of conventional choices and terminated by a Bayesian early stop criterion. These trajectories train an end-to-end Decision Transformer that selects the next query so as to improve the ultimate objective, following a dense training sparse learning paradigm: the transformer is trained on abundant simulated data, while a limited number of real evaluations refine the GPs online. On synthetic and real-world benchmarks, our method attains the best or near-best final simple regret against standard, lookahead, trust-region and amortized BO baselines, with the largest gains in high-dimensional settings. Ablations attribute the gains jointly to region-of-interest filtering and the learned policy, and matched-budget comparisons against explicit two-step lookahead acquisitions show that the advantage is not shared by lookahead alone.

Fengxue Zhang, Yuxin Chen

Department of Computer Science University of Chicago Chicago, IL 60637

Bayesian Optimization Learning to Optimize Decision Transformer Regret Minimization

May 6, 2025cs.LG

Sufficient Decision Proxies for Decision-Focused Learning

When solving optimization problems under uncertainty with contextual data, utilizing machine learning to predict the uncertain parameters' values is a popular and effective approach. Decision-focused learning (DFL) aims at learning a predictive model such that decision quality, instead of prediction accuracy, is maximized. Common practice is to predict a single scenario representing the uncertain parameters, implicitly assuming that there exists a deterministic problem approximation (proxy) that allows for optimal decision-making. The opposite has also been considered, where the underlying distribution is estimated with a parameterized distribution. However, little is known about when either choice is valid. This paper investigates for the first time problem properties that justify using a certain decision proxy. Using this, we present alternative decision proxies for DFL, with little or no compromise on the complexity of the learning task. We show the effectiveness of presented approaches in experiments on continuous and discrete problems, as well as problems with uncertainty in the objective function and in the constraints.

Noah Schutte, Grigorii Veviurko, Krzysztof Postek +1

Delft University of Technology · Independent Researcher

Stochastic Optimization Learning to Optimize Decision-Focused Learning Decision-Making under Uncertainty

Mar 31, 2025cs.NI

Traffic Engineering in Large-scale Networks with Generalizable Graph Neural Networks

Traffic Engineering (TE) in large-scale networks like cloud Wide Area Networks (WANs) and Low Earth Orbit (LEO) satellite constellations is a critical challenge. Although learning-based approaches have been proposed to address the scalability of traditional TE algorithms, their practical application is often hindered by a lack of generalization, high training overhead, and a failure to respect link capacities. This paper proposes TELGEN, a novel TE algorithm that learns to solve TE problems efficiently in large-scale network scenarios, while achieving superior generalizability across diverse network conditions. TELGEN is based on the novel idea of transforming the problem of "predicting the optimal TE solution" into "predicting the optimal TE algorithm", which enables TELGEN to learn and efficiently approximate the end-to-end solving process of classical optimal TE algorithms. The learned algorithm is agnostic to the exact underlying network topology or traffic patterns, and is able to very efficiently solve TE problems given arbitrary inputs and generalize well to unseen topologies and demands. We train and evaluate TELGEN with random and real-world topologies, with networks of up to 5000 nodes and 3.6x10^6 links in testing. TELGEN shows less than 3% optimality gap while ensuring feasibility in all testing scenarios, even when the test network has 2-20x more nodes than the largest training network. It also saves up to 84% TE solving time than traditional interior-point method, and reduces up to 79.6% training time per epoch than the state-of-the-art learning-based algorithm.

Fangtong Zhou, Xiaorui Liu, Ruozhou Yu +1

Department of Computer Science, North Carolina State University, Raleigh, NC, 27606, USA · School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ, 85287, USA

Graph Neural Networks Learning to Optimize

May 29, 2024cs.NE

MEGO: Learning Mixture-of-Experts for General-Purpose Binary Optimization

Discrete optimization is ubiquitous in science and engineering. The vast array of existing discrete optimization problems, coupled with the continuous emergence of new ones, necessitates off-the-shelf optimizers capable of generating high-quality solutions for a large variety of optimization problems. This article introduces MEGO, a novel general-purpose neural optimizer for binary optimization under the black-box setting, intended for broad applicability across diverse binary optimization problem classes with minimal problem-specific customization. MEGO comprises a mixture-of-experts trained without domain knowledge. When presented with a new problem instance to solve, it employs a routing policy to dynamically activate the most relevant expert models to generate high-quality solutions. The strong generalization capability of MEGO is demonstrated on six problem classes from different disciplines, including classic problems and real-world applications. Trained solely on classic problems, MEGO effectively generalizes to unseen and complex real-world problem classes, significantly outperforming widely-used general-purpose optimizers in both solution quality and efficiency. Furthermore, MEGO provides a computational approach for quantifying similarity between optimization problems and classifying them, which is fundamentally different from the conventional analysis-based problem classification.

Shengcai Liu, Zhiyuan Wang, Yew-Soon Ong +2

Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China · College of Computing & Data Science, Nanyang Technological University, Singapore 639798 · School of Data Science, Lingnan University, Hong Kong, China

Black-Box Optimization Mixture of Experts Learning to Optimize Neural Combinatorial Optimization

Date pendingcs.LG

Generalization Guarantees on Data-Driven Tuning of Gradient Descent with Langevin Updates

We study learning to learn through the lens of hyperparameter tuning. We propose the Langevin Gradient Descent Algorithm (LGD), which approximates the mean of the posterior distribution defined by the loss function and regularizer of a regression task with convex objective. For classification tasks, the LGD algorithm estimates the posterior probabilities of each class on the test set. We prove the existence of an optimal hyperparameter configuration for which the LGD algorithm achieves the Bayes' optimal solution for squared loss on regression tasks, and for which LGD closely approximates the posterior probabilities for well-specified classification tasks. Subsequently, we study generalization guarantees on meta learning optimal hyperparameters for the LGD algorithm from a given set of tasks in the data-driven setting. For a number of parameters

d

and hyperparameter dimension

h

, we show a pseudo-dimension bound of

O(dh)

, up to logarithmic terms under mild assumptions on LGD. This matches the dependence of the bounds on number of parameters obtained in prior work for linear regression using the elastic net, which only allows for

h=2

hyperparameters, and extends their bounds to regression on convex loss. Compared to bounds on regularized logistic regression that allow for only

h=1

hyperparameter, our bounds improve greatly on the dependence on samples per task at the cost of worse dependence on the number of parameters by accounting for hardware-aware procedures. Finally, we show empirical evidence of the success of LGD and the meta learning procedure for few-shot learning on linear and logistic regression using synthetically created datasets.

Saumya Goyal, Rohith Rongali, Ritabrata Ray +1

Machine Learning Department, Carnegie Mellon University · Electrical and Computer Engineering Department, Carnegie Mellon University.

Meta-Learning Gradient Descent Learning to Optimize Statistical Learning Theory Hyperparameter Optimization

Date pendingcs.LG

Code-to-Harness: Distilling Black-Box Optimizers from Self-Play

Can an agent learn a numerical search strategy through executable practice and then transfer that strategy as text? We study low-budget black-box optimization, where unaided language models remain well below strong classical optimizers. During development, an agent repeatedly writes and evaluates optimizer programs. It then distills the resulting program and practice record once into a 197-word primary Harness A, which is frozen before evaluation. Harness A reduces Gemini Flash regret by 48% in an independent

N=30

study (

p<.001

), enters the GP-BO performance range on the practice family, and lowers mean regret on all three held-out BBOB landscapes. The same text improves every tested Gemini executor and transfers to Claude Sonnet, reducing regret by 43% and 49% (

p\leq.005

). An independent end-to-end replication produces Harness B, a different program and text at the same performance tier. The same framework also attains the lowest regret on a sealed YouTube reward-tuning production benchmark. Executable practice is thus a viable way to discover a search policy, and language a portable medium for deploying it.

Yi Wu, Zheng Ren, Zhiyu Hu +8

Google Mountain View, USA

Black-Box Optimization Large Language Model-Guided Optimization Learning to Optimize LLM-Based Program Synthesis