Bilevel Optimization

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Overview

Bilevel optimization models decisions in two levels: an outer problem evaluates choices using the solution of an inner problem, as in hyperparameter tuning, data selection, meta-learning, and neural architecture search. Common approaches differentiate through inner optimization using unrolling or implicit hypergradients, while single-loop stochastic, penalty-based, and derivative-free methods aim to reduce computation and handle larger or black-box problems. Applications also use the framework for decision-focused learning, reinforcement learning, and strategic settings where one agent responds to another. A central challenge is making these methods efficient and reliable when the inner problem is nonconvex or has multiple solutions, while establishing useful convergence and generalization guarantees without restrictive assumptions.

Latest papers

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88 papers12 papers in the last four weeks, up 20% on the four weeks before. 0.1% of all new papers.

  1. Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems

    May 8, 2026Yiyang Shen, Yutian He, Weiran Wang +1Min-Max OptimizationBilevel Optimization

    University of Iowa

  2. When Losses Align: Gradient-Based Composite Loss Weighting for Efficient Pretraining

    May 8, 2026Ivan Karpukhin, Andrey SavchenkoSelf-Supervised Pre-TrainingAdaptive Loss Weighting

    Sber AI Lab · HSE University ISP RAS Research Center for Trusted Artificial Intelligence

  3. Differentially Private Auditing Under Strategic Response

    May 8, 2026Florian A. D. BurnatPrivacy AuditingAlgorithmic Auditing

    University of Bath

  4. Bilevel Graph Structure Learning, Revisited: Inner-Channel Origins of the Reported Gain

    May 8, 2026Minkyoung Kim, Beakcheol JangGraph Structure LearningGraph Neural Networks

    Graduate School of Information, Yonsei University

  5. Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models

    May 7, 2026Shivaram Subramanian, Zhengliang Xue, Markus Ettl +2Large Language Model-Guided OptimizationDiscrete Choice Modeling

    IBM T.J. Watson Research Center Yorktown Heights, New York, 10598, U.S.A.

  6. One Algorithm, Two Goals: Dual Scoring for Parameter and Data Selection in LLM Fine-Tuning

    May 7, 2026Xinrui Chen, Liu Yang, Ou WuSupervised Fine-TuningLLM Fine-Tuning

    Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences · College of Intelligence and Computing, Tianjin University

  7. Adversarial Co-Evolution of Malware and Detection Models: A Bilevel Optimization Perspective

    Apr 24, 2026Olha Jurečková, Martin Jureček, Matouš Kozák +1Adversarial AttacksAdversarial Robustness

    Faculty of Information Technology, Czech Technical University in Prague, Th´akurova 9, Prague, 16000, Czech Republic

  8. On the Stability and Generalization of First-order Bilevel Minimax Optimization

    Apr 22, 2026Xuelin Zhang, Peipei YuanMin-Max OptimizationBilevel Optimization

    College of Informatics, Huazhong Agricultural University, Wuhan, 430070, China · School of Artificial Intelligence, Jianghan University, Wuhan, 430056, China

  9. Bilevel Optimization of Agent Skills via Monte Carlo Tree Search

    Apr 17, 2026Chenyi Huang, Haoting Zhang, Jingxu Xu +2Large Language Model-Guided OptimizationLLM Agent Skill Learning

    Department of Mathematics National University of Singapore Singapore · Department of Industrial Engineering and Operations Research University of California at Berkeley CA, USA · Department of Decision, Operation and Technology The Chinese University of Hong Kong CHINA

  10. Bilevel Late Acceptance Hill Climbing for the Electric Capacitated Vehicle Routing Problem

    Apr 14, 2026Yinghao Qin, Mosab Bazargani, Edmund K. Burke +3Vehicle RoutingBilevel Optimization

    Centre for Intelligent Transport, QMUL, London, U.K. · School of Computer Science and Engineering, Bangor University, Bangor, U.K. · Department of Computer Science, Evolutionary Computation Group, CINVESTAV-IPN, Mexico City, Mexico. +2

  11. BEAM: Bi-level Memory-adaptive Algorithmic Evolution for LLM-Powered Heuristic Design

    Apr 14, 2026Chuyang Xiang, Yichen Wei, Jiale Ma +2Automated Heuristic DesignLarge Language Model-Guided Optimization

  12. Differentiable Environment-Trajectory Co-Optimization for Safe Multi-Agent Navigation

    Apr 8, 2026Zhan Gao, Gabriele Fadini, Stelian Coros +1Robot NavigationSafe Robot Navigation

    Department of Computer Science and Technology, University of Cambridge, UK · Zurich University of Applied Sciences, ZHAW, Winterthur, Swizerland · Computational Robotics Lab, Department of Computer Science, ETH Zurich, Switzerland

  13. Fine-grained Analysis of Stability and Generalization for Stochastic Bilevel Optimization

    Apr 5, 2026Xuelin Zhang, Hong Chen, Bin Gu +2Stochastic Bilevel OptimizationBilevel Optimization

    College of Informatics, Huazhong Agricultural University, Wuhan 430070, China · Engineering Research Center of Intelligent Technology for Agriculture, Ministry of Education, Wuhan 430070, China · School of Artificial Intelligence, Jilin University, Jilin 130012, China +2

  14. Accelerating Black-Box Bilevel Optimization with Rank-Based Upper-Level Value Function Approximation

    Apr 3, 2026Marc Ong, Youhei AkimotoBilevel OptimizationBlack-Box Optimization

    University of Tsukuba Tsukuba, Ibaraki, JAPAN · University of Tsukuba & RIKEN AIP Tsukuba, Ibaraki, JAPAN

  15. Efficient Bilevel Optimization with KFAC-Based Hypergradients

    Mar 31, 2026Disen Liao, Felix Dangel, Yaoliang YuKronecker-Factored ApproximationBilevel Optimization

    University of Waterloo · Vector Institute

  16. Bilevel Autoresearch: Meta-Autoresearching Itself

    Mar 24, 2026Yaonan Qu, Meng LuSelf-Improving AgentsAutonomous Research Agents

    Independent Researcher

  17. Strategic Infrastructure Design via Multi-Agent Congestion Games with Joint Placement and Pricing

    Mar 23, 2026Niloofar Aminikalibar, Farzaneh Farhadi, Maria ChliCongestion GamesMulti-Agent System Optimization

    Aston University, Birmingham, UK, B4 7ET

  18. Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization

    Mar 16, 2026Yanning Dai, Yuhui Wang, Dylan R. Ashley +1Robot Morphology-Control Co-DesignBilevel Optimization

    Center of Excellence for Generative AI, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia. · Dalle Molle Institute for Artificial Intelligence Research (IDSIA), Lugano, Switzerland. · Università della Svizzera italiana (USI), Lugano, Switzerland. +1

  19. Feed m Birds with One Scone: Accelerating Multi-task Gradient Balancing via Bi-level Optimization

    Mar 8, 2026Xuxing Chen, Yun He, Jiayi Xu +9Multi-Task LearningBilevel Optimization

    Meta

  20. Bi-level RL-Heuristic Optimization for Real-world Winter Road Maintenance

    Feb 27, 2026Yue Xie, Zizhen Xu, William Beazley +1Vehicle RoutingBilevel Optimization

    School of Science, Loughborough University, UK · Department of Engineering, University of Cambridge, UK · National Highways, 199 Wharfside St, Birmingham B1 1RN, UK

  21. On the Convergence of Single-Loop Stochastic Bilevel Optimization with Approximate Implicit Differentiation

    Feb 27, 2026Yubo Zhou, Luo Luo, Guang Dai +1Stochastic Bilevel OptimizationImplicit Differentiation

    Xi’an Jiaotong University · Fudan University · SGIT AI Lab

  22. Less is More: Convergence Benefits of Fewer Data Weight Updates over Longer Horizon

    Feb 23, 2026Rudrajit Das, Neel Patel, Meisam Razaviyayn +1Data Mixture OptimizationBilevel Optimization

    Google Research · EPFL · University of Southern California

  23. Understanding the Generalization of Bilevel Programming in Hyperparameter Optimization: A Tale of Bias-Variance Decomposition

    Feb 20, 2026Yubo Zhou, Jun Shu, Junmin Liu +1Hypergradient OptimizationHyperparameter Optimization

    School of Mathematics and Statistics and Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, 100190, Shaan’xi Province, P. R. China. · Pazhou Lab (Huangpu), Street, Guangzhou, Guangdong Province, P. R. China.

  24. Non-Stationary Functional Bilevel Optimization

    Jan 21, 2026Jason Bohne, Ieva Petrulionyte, Michael Arbel +2Bilevel OptimizationHyperparameter Optimization

    Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA · Inria, CNRS, Grenoble INP, LJK, Université Grenoble Alpes

  25. On the Condition Number Dependency in Bilevel Optimization

    Nov 27, 2025Lesi Chen, Jingzhao ZhangOracle ComplexityNonconvex Optimization

    IIIS, Tsinghua University

  26. Bilevel Data Curation for LLM Fine-tuning: Offline Selection and Online Self-Refining Generation

    Nov 26, 2025Quan Xiao, Yutong Xuan, Gaowen Liu +2Supervised Fine-TuningLLM Self-Refinement

    Cornell University · Cisco Research

  27. OFMU: Optimization-Driven Framework for Machine Unlearning

    Sep 26, 2025Sadia Asif, Mohammad Mohammadi AmiriBilevel OptimizationMachine Unlearning

    Rensselaer Polytechnic Institute

  28. A Provably Convergent Plug-and-Play Framework for Stochastic Bilevel Optimization

    May 2, 2025Tianshu Chu, Dachuan Xu, Wei Yao +2Stochastic Bilevel OptimizationBilevel Optimization

    Institute of Operations Research and Information Engineering, Beijing University of Technology · National Center for Applied Mathematics Shenzhen · National Center for Applied Mathematics Shenzhen, and Department of Mathematics, Southern University of Science and Technology +2