Bilevel Optimization

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7 papers in the last four weeks, up 17% on the four weeks before. 0.1% of all new papers.

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A Single-Loop, Constant-Batch First-Order Penalty Method for Stochastic Bilevel Optimization
Oct 5, 2026Xingyu Chen, Ming Yang, Quanqi Hu +1Bilevel Optimization
Department of Computer Science and Engineering Texas A&M University, College Station, USA
Smoothed Gradient Method for Nonconvex Federated Stochastic Bilevel Optimization
Oct 4, 2026Xinwen Zhang, Peiran Yu, Zhaosong Lu +1Bilevel Optimization Stochastic Convex Optimization
Temple University · University of Texas at Arlington · University of Minnesota
Optimal Stochastic Bilevel Optimization with First-Order Oracles
Oct 1, 2026Linxuan Pan, Junchi YangBilevel Optimization First Order Oracle Complexity
The Chinese University of Hong Kong, Shenzhen
Anchoring Adversarial Trajectories to Data Manifolds: A Bilevel Transfer Optimization Framework
Sep 30, 2026Yaohua Liu, Yifan Guo, Jiaxin GaoAdversarial Training Bilevel Optimization
The University of Hong Kong Hong Kong, China · International School of Information Science & Engineering Dalian University of Technology, Dalian, China · The Hong Kong Polytechnic University Hong Kong, China
Learning the Robustness Mechanism with Bilevel Optimization
Sep 28, 2026Yiyang Shen, Qihang Lin, Weiran WangDistributionally-Robust Optimization Learnability
Department of Informatics University of Iowa · Tippie College of Business University of Iowa · Department of Computer Science University of Iowa
A Light Bilevel Refinement Aligns Self-Supervised Representations for Stronger Task-Specific Learning
Sep 27, 2026Gustav Wagner Zakarias, Zheng-Hua TanSelf-Supervised Learning Bilevel Optimization
Aalborg University · Pioneer Centre for Artificial Intelligence, Denmark
Federated stochastic bilevel optimization with fully first-order gradients
Sep 14, 2026Yihan Zhang, Rohit Dhaipule, Chiu C Tan +2Bilevel Optimization Gradient Descent
1Temple University · 2Stony Brook University
CIDERS: Cloud-Edge LLM Collaborative Learning via Accelerating Personalized Bilevel Optimization
Sep 14, 2026Victor H. Chen, Hairui Yu, Stella K. Chung +1Edge Platforms Large Language Model Personalization
Disciplined Bilevel Programming
Sep 1, 2026Hao Zhu, Joschka BoedeckerBilevel Optimization Sequential Decision Making
IMBIT//BrainLinks-BrainTools · Department of Computer Science, University of Freiburg
Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization
Aug 31, 2026Jessica D. Elrefaei, Kaixun Hua, Seungbae Kim +2Bilevel Optimization Mixed-Integer Programming
Spec2Twin-Chain: Orchestrating Bi-Level Optimization with LLMs for Blockchain Digital Twin Construction
Aug 30, 2026Haoting Zhang, Haoxian Chen, Jiayuan Sheng +4Blockchain Invariant Synthesis
Haoting Zhang, Jiayuan Sheng, Haoxian Chen, Donglin Zhan, Zeyu Zheng, David D. Yao, and Wenpin Tang
Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level
Aug 13, 2026Yicong Jiang, Feihu HuangBilevel Optimization Multi-Objective Optimization
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China · College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China; and also with MIIT Key Laboratory of Pattern Analysis and Machine Intelligence, Nanjing, China
Learning with Bilevel-Minimax Optimization for Efficient and Reliable Transfer Attacks
Aug 12, 2026Yaohua Liu, Yifan Guo, Jiaxin GaoAdversarial Training Bilevel Optimization
The University of Hong Kong, Hong Kong SAR, China · International School of Information Science & Engineering, Dalian University of Technology, Dalian, China · The Hong Kong Polytechnic University, Hong Kong SAR, China
Efficient Hypergradient Descent for Inverse Reinforcement Learning
Aug 11, 2026Nikita Sevriukov, Anna Barabanova, Uliana Gagarina +4Offline Reinforcement Learning Reward Functions
HSE University Moscow, Russia
Beyond Post-Hoc Temperature Scaling: Bilevel Optimization for LLM Calibration
Aug 7, 2026Ruochen Jin, Zhanliang Wang, Zongyu Dai +2Overconfidence Loss Function
Dartmouth College, Hanover, NH · University of Pennsylvania, Philadelphia, PA · National University of Singapore, Singapore
Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization
Aug 4, 2026Joshua E. Hammond, Tyler A. Soderstrom, Brian A. Korgel +1Black-Box Optimization Bayesian Optimization
McKetta Department of Chemical Engineering, The University of Texas at Austin, 200 E. Dean Keaton St. Stop C0400, Austin, Texas 78712, USA · ExxonMobil Technology and Engineering, 22777 Springwoods Village Pkwy, Spring, Texas 77389, USA · Energy Institute, The University of Texas at Austin, 2304 Whitis Ave. Stop C2400, Austin, Texas 78712, USA +1
Partially-Observable Transmission Control for UAV-Enabled Federated Learning in IoT Networks
Aug 1, 2026Masoud Ghazikor, Zhou Ni, Morteza HashemiFederated Learning Power Allocation
Department of Electrical Engineering and Computer Science, University of Kansas
Sharper Analysis of Single-Loop Methods for Bilevel Optimization
Jul 11, 2026Yubo Zhou, Jun Shu, Luo Luo +4Bilevel Optimization Convergence
School of Mathematics and Statistics, Xi’an Jiaotong University · School of Data Science, Fudan University · 3SGIT AI Lab, State Grid Corporation of China +1
Functional Bilevel Optimization for Predictive Fairness
Jul 6, 2026Ieva Petrulionyte, Julien Mairal, Michael ArbelAlgorithmic Fairness Bilevel Optimization
Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
Bilevel Optimization for Neural Architecture Search
Jun 28, 2026Abhishek Shukla, Ankur Sinha, Faiz HamidBilevel Optimization Neural Architecture Search
Department of Management Sciences, IIT Kanpur, India · Krishnamurthy Tandon School of AI, IIM Ahmedabad, India
Agentic AI for Bilevel Long-Term Optimization of Policy-Driven Physical Layer Systems
Jun 23, 2026Bingnan Xiao, Chenhao Yang, Wei Ni +2Agentic Optimization Bilevel Optimization
Key Laboratory of EMW Information (MoE), College of Future Information Technology, Fudan University, Shanghai 200433, China · James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, U.K. · School of Engineering, Edith Cowan University, Perth, WA 6027, Australia +1
Constrained Variable Projection for Structured Problems
Jun 22, 2026Emanuele Zangrando, Sara Venturini, Francesco Rinaldi +1Bilevel Optimization Projection
Gran Sasso Science Institute, L’Aquila, Italy. · MOBS Lab, Northeastern University, Boston, USA. · University of Padova, Padova, Italy. +1
Distribution-Aware Robust Bilevel Optimization: Quantile-Guided Huber Updates in Two-Timescale Stochastic Approximation
Jun 21, 2026Zhiyu Li, Xi Xuan, Davide CarboneBilevel Optimization Stochastic Approximation
University of Science and Technology of China Hefei, China · City University of Hong Kong Hong Kong SAR, China · Laboratoire de Physique de l’École Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris Paris, France
Escaping the Variance Trap: Jacobian-Free Dynamics for Root-Finding Bilevel Optimization
Jun 21, 2026Zhiyu Li, Xi Xuan, Davide CarboneBilevel Optimization Stochastic Approximation
University of Science and Technology of China · City University of Hong Kong · Laboratoire de Physique de l’École Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris
DUET: Decentralized Bilevel Optimization without Lower-Level Strong Convexity
Jun 19, 2026Zhen Qin, Zhuqing Liu, Songtao Lu +2Bilevel Optimization Decentralized Optimization
Department of Electrical and Computer Engineering, The Ohio State University · Department of Computer Science and Engineering, University of North Texas · Department of Computer Science and Engineering, The Chinese University of Hong Kong
Federated Bilevel Performative Prediction
Jun 18, 2026Liangxin Qian, Chang Liu, Xuanyu Cao +2Bilevel Optimization Distribution Shifts
College of Computing and Data Science, Nanyang Technological University, 639798, Singapore · Innovation and Management Center, School of Software Technology (Ningbo), Zhejiang University, 315100, China · School of Electrical Engineering & Computer Science, Washington State University, Pullman, WA 99164, USA.
Two-Phase Bilevel Search for the Moving-Target Traveling Salesman Problem with Moving Obstacles
Jun 17, 2026Allen George Philip, Anoop Bhat, Sivakumar Rathinam +1Salesman Problem Bilevel Optimization
Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123 · Robotics Institute, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA · Mechanical Engineering, and Computer Science and Engineering, Texas A&M University, College Station, TX 77843-3123
Evolutionary Bilevel Reward Shaping for Generalization in Reinforcement Learning
Jun 15, 2026Ekasit Usaratniwart, Xilin Gao, Marc Ong +1Potential-Based Reward Shaping Bilevel Optimization
University of Tsukuba, Tsukuba, Japan · RIKEN Center for Advanced Intelligence Project, Tokyo, Japan
Mixed-Categorical Black-Box Optimization via Information-Geometric Bilevel Decomposition
Jun 11, 2026Marc Ong, Shinichi Shirakawa, Youhei AkimotoBilevel Optimization Black-Box Optimization
University of Tsukuba, Tsukuba, Japan · Yokohama National University, Yokohama, Japan · RIKEN Center for Advanced Intelligence Project, Tokyo, Japan
S $^3$ LDBO: A Snapshot Single-Loop Algorithm for Decentralized Bilevel Optimization
May 29, 2026Chao Yin, Youran Dong, Shiqian Ma +2Bilevel Optimization Meta-Learning
School of Mathematics, Hohai University, Nanjing, P. R. China · School of Mathematics, Nanjing University, Nanjing, P. R. China · Department of Computational Applied Mathematics and Operations Research, Rice University, Houston, USA
BadBone: Backdoor Attacks Against Backbone Models in Visual Prompt Learning
May 29, 2026Ziqing Yang, Rui Wen, Xinlei He +3Model-Agnostic Defense Bad
1CISPA Helmholtz Center for Information Security · Institute of Science Tokyo · 3Wuhan University +1
A Surveillance Evasion Game with Continuous Sensor Redeployment via Bilevel Optimization
May 27, 2026Jaehyeok Kim, Kartik A. Pant, Joseph Kinerson +4Multi-Uav Optimal Sensor Placement
School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906
Detectability in Diversity: Improved Canary Crafting for Privacy Auditing in One Run
May 26, 2026Mathieu Dagréou, Aurélien BelletMembership Inference Attacks Fairness Audits
PreMeDICaL team, Inria · Idesp, Inserm, Univ. de Montpellier
Bilevel Optimization over Saddle Points of Zero-Sum Markov Games
May 26, 2026Zihao Zheng, Irwin King, Songtao LuBilevel Optimization Mean Field Games
Department of Computer Science and Engineering, The Chinese University of Hong Kong · Shun Hing Institute of Advanced Engineering, The Chinese University of Hong Kong
Bilevel Optimization of Synthetic Trajectories for Multi-Turn LLM Fine-Tuning
May 23, 2026Shresth Verma, Mauricio Tec, Cheol Woo Kim +2Large Language Model Fine-Tuning Offline Reinforcement Learning
Harvard University Cambridge, MA · Georgia Institute of Technology Atlanta, GA
Semiparametric Efficient Bilevel Gradient Estimation
May 20, 2026Fares El Khoury, Houssam Zenati, Nathan Kallus +2Bilevel Optimization Influence Function
Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK · Gatsby Computational Neuroscience Unit, University College London · Cornell University +1
Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization
May 19, 2026Yutong Chao, Xudong Sun, Konstantin Riedl +2Bilevel Optimization Convex Optimization
Department of Computer Science Technical University of Munich · Munich Institute of Robotics and Machine Intelligence Technical University of Munich · Mathematical Institute University of Oxford
A Two-Phase Adaptive Balanced Penalty Method for Controllable Pareto Front Learning under Split Feasibility Conditions
May 19, 2026Nguyen Viet Hoang, Dung D. Le, Tran Ngoc ThangQuadratic Slack Penalty Pareto Frontier
Balancing Knowledge Distillation for Imbalance Learning with Bilevel Optimization
May 18, 2026Anh B. H. Nguyen, Ba Tho Phan, Viet Cuong TaBalanced Learning Knowledge Distillation
VNU University of Engineering and Technology, Hanoi, Vietnam
Efficient Bilevel Optimization for Meta Label Correction in Noisy Label Learning
May 18, 2026Ba Hoang Anh Nguyen, Viet Cuong TaNoisy Labels Bilevel Optimization
Human-Machine Interaction Laboratory, VNU University of Engineering and Technology, Hanoi, Vietnam
Learning Bilevel Policies over Symbolic World Models for Long-Horizon Planning
May 15, 2026Dillon Z. Chen, Till Hofmann, Toryn Q. Klassen +1Long-Horizon Planning Imitation Learning
1Vector Institute · University of Toronto · 3LAAS-CNRS +2
IGT-OMD: Implicit Gradient Transport for Decision-Focused Learning under Delayed Feedback
May 12, 2026Benjamin Amoh, Geoffrey G. Parker, Wesley MarreroBilevel Optimization Optimal Regret
Thayer School of Engineering, Dartmouth College
BROS: Bias-Corrected Randomized Subspaces for Memory-Efficient Single-Loop Bilevel Optimization
May 11, 2026Hengrui Zhang, Boao Kong, Engao Zhang +1Bilevel Optimization Subspace
1Sichuan University · 2Peking University
FocuSFT: Bilevel Optimization for Dilution-Aware Long-Context Fine-Tuning
May 11, 2026Zehua Pei, Hui-Ling Zhen, Xianzhi Yu +3Efficient Long-Context Inference Model Fine-Tuning
The Chinese University of Hong Kong · Huawei Technologies Co., Ltd
Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets
May 9, 2026Saeed Masiha, Zebang Shen, Negar Kiyavash +1Bilevel Optimization Flat Minima
EPFL School of Management of Technology, Station 5, 1015 Lausanne, Switzerland · ETH Department of Computer Science, Universitätstrasse 6, 8092 Zürich, Switzerland
A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimization
May 9, 2026Zhiyao Zhang, Myeung Suk Oh, Zhen Qin +3Bilevel Optimization Multi-Objective Optimization
Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA · Meta Platforms, Inc., Menlo Park, CA, USA.
Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems
May 8, 2026Yiyang Shen, Yutian He, Weiran Wang +1Bilevel Optimization Convex Optimization
University of Iowa
When Losses Align: Gradient-Based Composite Loss Weighting for Efficient Pretraining
May 8, 2026Ivan Karpukhin, Andrey SavchenkoPretraining Backpropagation
Sber AI Lab · HSE University ISP RAS Research Center for Trusted Artificial Intelligence
Breaking QAOA's Fixed Target Hamiltonian Barrier: A Fully Connected Quantum Boltzmann Machine via Bilevel Optimization
May 8, 2026Jun LiuQuantum Approximate Optimization Algorithm Qubit
School of Economics, Hunan University of Finance and Economics, Changsha 410205, China
Causal-Aware Foundation-Model for Bilevel Optimization in Discrete Choice Settings
May 7, 2026Shivaram Subramanian, Zhengliang Xue, Markus Ettl +2Discrete Choice Models Dynamic Pricing
IBM T.J. Watson Research Center Yorktown Heights, New York, 10598, U.S.A.
ReActor: Reinforcement Learning for Physics-Aware Motion Retargeting
May 7, 2026David Müller, Agon Serifi, Sammy Christen +3Cross-Embodiment Retargeting Motion Imitation
Disney Research, Switzerland
Instance-Aware Parameter Configuration in Bilevel Late Acceptance Hill Climbing for the Electric Capacitated Vehicle Routing Problem
May 1, 2026Yinghao Qin, Xinwei Wang, Mosab Bazargani +1Vehicle Routing Problem Metaheuristics
Centre for Intelligent Transport Queen Mary, University of London London, UK · School of Computer Science and Engineering Bangor University Bangor, UK
Interactive Inverse Reinforcement Learning of Interaction Scenarios via Bi-level Optimization
May 1, 2026Yue Mao, Shicheng Liu, Siyuan Xu +1Offline Reinforcement Learning Reward Functions
Department of Mechanical Engineering, Pennsylvania State University · Department of Electrical Engineering, Pennsylvania State University
Bi-Level Optimization for Contact and Motion Planning in Rope-Assisted Legged Robots
Apr 29, 2026Ruben Malacarne, Ioannis Tsikelis, Enrico Mingo Hoffman +1Locomotion Motion Planning
Dipartimento di Ingegneria e Scienza dell’Informazione (DISI), University of Trento · Inria, Universit´e de Lorraine, CNRS, 54000 Nancy, France
FlowBot: Inducing LLM Workflows with Bilevel Optimization and Textual Gradients
Apr 29, 2026Hongyeon Yu, Young-Bum Kim, Yoon KimLarge Language Model Workflows Agentic Workflow Design
Naver Search US · Massachusetts Institute of Technology
Adversarial Co-Evolution of Malware and Detection Models: A Bilevel Optimization Perspective
Apr 24, 2026Olha Jurečková, Martin Jureček, Matouš Kozák +1Malware Model-Agnostic Defense
Faculty of Information Technology, Czech Technical University in Prague, Th´akurova 9, Prague, 16000, Czech Republic
On the Stability and Generalization of First-order Bilevel Minimax Optimization
Apr 22, 2026Xuelin Zhang, Peipei YuanBilevel Optimization Generalization Bounds
College of Informatics, Huazhong Agricultural University, Wuhan, 430070, China · School of Artificial Intelligence, Jianghan University, Wuhan, 430056, China
Meta Additive Model: Interpretable Sparse Learning With Auto Weighting
Apr 22, 2026Xuelin Zhang, Xinyue Liu, Lingjuan Wu +1Generalized Linear Model Reweighting
College of Informatics, Huazhong Agricultural University, Wuhan, China
S2MAM: Semi-supervised Meta Additive Model for Robust Estimation and Variable Selection
Apr 21, 2026Xuelin Zhang, Hong Chen, Yingjie Wang +2Semi-Supervised Learning Regularization
Huazhong Agricultural University · China University of Petroleum (East China) · Xi’an Jiaotong University +1
SOCIA-EVO: Automated Simulator Construction via Dual-Anchored Bi-Level Optimization
Apr 19, 2026Yuncheng Hua, Sion Weatherhead, Mehdi Jafari +2Alphaevolve Simulation-Based Reinforcement Learning
School of Computer Science and Engineering, University of New South Wales, Australia

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A Single-Loop, Constant-Batch First-Order Penalty Method for Stochastic Bilevel Optimization

Xingyu Chen, Ming Yang, Quanqi Hu, Tianbao Yang

Department of Computer Science and Engineering Texas A&M University, College Station, USA

Bilevel Optimization

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Recent advances in penalty-based methods for stochastic bilevel optimization (SBO) have eliminated the need for second-order derivative oracles. However, for stochastic nonconvex-strongly convex bilevel problems, existing first-order methods typically rely on nested loops and/or large batch sizes for attaining

O(ε^{-6})

O(ε^{-4})

sample complexity under standard bounded-variance assumption or mean-square smoothness assumption. Achieving these rates with a single-loop penalty method and a constant batch size remains challenging due to a large penalty value needed for an accurate approximation. To address this challenge, we develop a stochastic SIngle-loop COnstant-Batch first-order penalty method (SICO) that combines two complementary ingredients. First, it performs one stochastic-gradient update per-iteration for both the original lower-level and penalized problems, with a projection that controls the separation between their iterates. Second, it applies an exponential moving average to stabilize the upper-level gradient estimator. We show that this combination achieves

O(ε^{-6})

sample complexity using only

O(1)

stochastic-gradient samples per iteration under unbiased, bounded-variance stochastic gradients. Under the additional mean-square smoothness assumption on the lower-level stochastic gradients, the same algorithm improves the complexity to

O(ε^{-4})

also with

O(1)

batch size. To the best of our knowledge, this is the first work to match the best-known convergence rate for fully first-order SBO methods using a single loop and a constant batch size. This result addresses an open problem posed in the literature.

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