Mirror Descent

Ask about this topic

Overview

Mirror descent is a family of optimization methods that uses a chosen distance geometry, rather than ordinary Euclidean steps, to shape updates. Common approaches include entropic mirror descent and exponentiated-gradient updates for simplex constraints, barrier-based methods, and optimistic mirror descent for games. The methods are studied in settings such as online learning with sparse losses or bandit feedback, constrained stochastic optimization, equilibrium learning, optimal transport, and neural-network training. Choosing geometry well can improve regret or convergence, but boundary behavior, initialization sensitivity, and guarantees for the final iterate remain important challenges.

Latest papers

CardsList

23 papers1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. Average-and Last-Iterate Lower Bounds for Optimistic Matrix Mirror-Prox in Quantum Zero-Sum Games

    Sep 30, 2026Yiheng Su, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Pucheng XiongLast-Iterate ConvergenceOracle Complexity

    Department of Computer Sciences, University of Wisconsin-Madison

  2. Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problems

    Sep 25, 2026Joanna Marks, Gabriel Rioux, Riccardo PasseggeriGradient DescentMirror Descent

    ⋆Denotes equal contribution to this work.

  3. Independent Reinforcement Learning in Discounted Markov Games

    Sep 1, 2026Asrin Efe Yorulmaz, Ugur Aydin, Tamer BasarReinforcement LearningGame Theory

    Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA

  4. Mirror descent algorithms with logarithmic barriers

    Aug 24, 2026Alberto De Marchi, Yura Malitsky, Adrien B. TaylorMirror Descent

    University of the Bundeswehr Munich, Germany · Faculty of Mathematics, University of Vienna, Austria · Inria, DI ENS, CNRS, PSL Research University, France

  5. Establishing Boundary KKT Convergence of Mirror Descent through Reparameterization

    Aug 7, 2026Kuangyu Ding, Kim-Chuan TohNonconvex OptimizationMirror Descent

    School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA. · Department of Mathematics, National University of Singapore, Singapore 119076.

  6. Non-KKT Accumulation in Entropic Mirror Descent

    Aug 3, 2026Kuangyu Ding, Kim-Chuan TohOptimization Convergence AnalysisMirror Descent

    School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA. · Department of Mathematics and Institute of Operations Research and Analytics, National University of Singapore, Singapore 119076.

  7. Incremental Learning in Mirror Flows

    Jun 22, 2026Raphaël Berthier, Loucas Pillaud-VivienContinual LearningMirror Descent

    Sorbonne Université, Inria, Centre Inria de Sorbonne Université, Paris, France · CERMICS, CNRS, ENPC, Institut Polytechnique de Paris, Marne-la-Vallée, France

  8. Mirror Descent Beyond Euclidean Stability: An Exponential Separation in Initialization Sensitivity

    Jun 9, 2026Shira Vansover-Hager, Matan Schliserman, Ofir Schlisselberg +1Algorithmic StabilityMirror Descent

    Blavatnik School of Computer Science and AI, Tel Aviv University · Google Research

  9. DICE: Entropy-Regularized Equilibrium Selection for Stable Multi-Agent LLM Coordination

    Jun 6, 2026Yi Xie, Zhanke Zhou, Chentao Cao +2Multi-Agent CoordinationGame Theory

    Department of Electrical & Computer Engineering University of Arizona Tucson, AZ 85721-0104, USA · Department of Computer Science Hong Kong Baptist University Kowloon Tong, Hong Kong SAR

  10. Bregman meets Lévy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time

    Jun 2, 2026Pierre-Louis Cauvin, Panayotis MertikopoulosStochastic OptimizationStochastic Differential Equations

    Univ. Grenoble Alpes, CNRS, Inria, Grenoble INP, LIG, 38000 Grenoble, France.

  11. HORST: Composing Optimizer Geometries for Sparse Transformer Training

    May 20, 2026Tom Jacobs, Rohan Jain, Rebekka BurkholzDeep Learning OptimizationTransformer

    CISPA Helmholtz Center for Information Security

  12. φφ-Balancing for Mixture-of-Experts Training

    May 14, 2026Lizhang Chen, Jonathan Li, Qi Wang +5Expert Load BalancingMirror Descent

    University of Texas at Austin · 2Northwestern University.

  13. Concave Statistical Utility Maximization Bandits via Influence-Function Gradients

    Apr 24, 2026Matías Carrasco, Alejandro CholaquidisMulti-Armed BanditsMirror Descent

    Universidad ORT Uruguay Montevideo, Uruguay · Facultad de Ciencias Universidad de la República Montevideo, Uruguay

  14. The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback

    Apr 17, 2026Côme Fiegel, Pierre Ménard, Tadashi Kozuno +2Nash EquilibriumLast-Iterate Convergence

    ENSAE Paris - CREST, Palaiseau, France · Inria - FairPlay · ENS Lyon, Lyon, France +3

  15. Transformers Learn Latent Mixture Models In-Context via Mirror Descent

    Apr 12, 2026Francesco D'Angelo, Nicolas FlammarionIn-Context LearningTransformer Attention

    TML Lab, EPFL, Switzerland

  16. State-space models through the lens of ensemble control

    Mar 13, 2026Ye Feng, Jianfeng LuMirror DescentOptimal Control

  17. Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning

    Mar 9, 2026Andrzej Cichocki, Piergiulio TempestaMirror Descent

  18. Never Saddle for Reparameterized Steepest Descent as Mirror Flow

    Mar 2, 2026Tom Jacobs, Chao Zhou, Rebekka BurkholzNeural Network Training DynamicsGradient Descent Dynamics

    CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

  19. Mirror Descent-Type Algorithms for the Variational Inequality Problem with Functional Constraints

    Feb 24, 2026Mohammad S. Alkousa, Fedor S. Stonyakin, Belal A. Alashqar +1Mirror DescentConstrained Optimization

    Innopolis University, Innopolis, Universitetskaya Str., 1, 420500, Russia. · Moscow Institute of Physics and Technology, 9 Institutsky lane, Dolgoprudny, 141701, Russia. · V. I. Vernadsky Crimean Federal University, 4 Academician Vernadsky Avenue, Simferopol, 295007, Republic of Crimea, Russia.

  20. Implicit Bias and Convergence of Matrix Stochastic Mirror Descent

    Feb 22, 2026Danil Akhtiamov, Reza Ghane, Omead Pooladzandi +1Mirror DescentStochastic Optimization Convergence

    Electrical Engineering, Caltech, Pasadena, CA

  21. Block-Norm Geometries for Online Mirror Descent with Sparse Losses

    Feb 13, 2026Swati Gupta, Jai Moondra, Mohit SinghOnline Convex OptimizationOnline Mirror Descent

    MIT · CMU · Georgia Tech

  22. Basic Inequalities for First-Order Optimization with Applications to Statistical Risk Analysis

    Dec 31, 2025Seunghoon Paik, Kangjie Zhou, Matus Telgarsky +1Early StoppingGradient Descent

    University of California, Berkeley · Columbia University · New York University

  23. Mirror Descent Linearized Augmented Lagrangian Methods for Nonconvex Constrained Stochastic Zeroth-Order Optimization

    Apr 13, 2025Qiankun Shi, Han Yuan, Xiao Wang +1Zeroth-Order OptimizationAugmented Lagrangian Method

    Sun Yat-sen University, Guangzhou, 510006, China · Pengcheng Laboratory, Shenzhen, 518066, China · Sun Yat-sen University, Guangzhou, 518066, China +1