Risk-Averse Wasserstein Distributionally Robust Online Learning
Not on the map. Why?
Abstract (arXiv)
We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm is well understood in the offline setting through Wasserstein Distributionally Robust Optimization (DRO), its online extension poses significant challenges in convergence. In this paper, we formulate the problem as an online saddle-point stochastic game between a decision maker and an adversary selecting worst-case distributions, and propose a general framework that converges to a robust Nash equilibrium coinciding with the solution of the corresponding offline Wasserstein DRO problem.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 32 of its 55 references that are in the map. First posted on arXiv 23 Feb 2026.
Builds on
32 of 55 references.
References · 32
- 2014Explaining and Harnessing Adversarial Examplescited by 7,287
- 2016Adversarial Machine Learning at Scalecited by 934
- 2021Generalized Out-of-Distribution Detection: A Surveycited by 796
- 2018Generalizing to Unseen Domains via Adversarial Data Augmentationcited by 451
- 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 407
- 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
- 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 285
- 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 182
- 2021On the Convergence and Robustness of Adversarial Trainingcited by 127
- 2014Algorithms for CVaR Optimization in MDPscited by 98
- 2017Regularization via Mass Transportationcited by 79
- 2020Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionalitycited by 49
20 more
- 2014Faster Rates for the Frank-Wolfe Method over Strongly-Convex Setscited by 42
- 2020An Online Method for A Class of Distributionally Robust Optimization with Non-Convex Objectivescited by 42
- 2019Model-Based Reinforcement Learning with Adversarial Training for Online Recommendationcited by 33
- 2018Theoretical Analysis of Adversarial Learning: A Minimax Approachcited by 31
- 2022Minimax Regret Optimization for Robust Machine Learning under Distribution Shiftcited by 31
- 2014Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Banditscited by 26
- 2016Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measurecited by 20
- 2022Distributionally Robust End-to-End Portfolio Constructioncited by 17
- 2023On Dynamic Programming Decompositions of Static Risk Measures in Markov Decision Processescited by 17
- 2023Outlier-Robust Wasserstein DROcited by 16
- 2020Principled learning method for Wasserstein distributionally robust optimization with local perturbationscited by 14
- 2017Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimizationcited by 11
- 2014Oracle-Based Robust Optimization via Online Learningcited by 9
- 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimizationcited by 8
- 2024Robust Distribution Learning with Local and Global Adversarial Corruptionscited by 5
- 2016Online First-Order Framework for Robust Convex Optimizationcited by 2
- 2023Data-driven Distributionally Robust Optimization over Timecited by 2
- 2025Wasserstein Distributionally Robust Regret Optimizationcited by 2
- 2021First-order algorithms for robust optimization problems via convex-concave saddle-point Lagrangian reformulationcited by 1
- 2024A Max-Min-Max Algorithm for Large-Scale Robust Optimizationcited by 1
Built on by
Not cited yet.