# Risk-Averse Wasserstein Distributionally Robust Online Learning

arXiv: https://arxiv.org/abs/2602.20403 · HTML: https://mlsanity.com/paper/2602.20403/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 55 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 30 of 32)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Generalizing to Unseen Domains via Adversarial Data Augmentation](https://mlsanity.com/paper/1805.12018/) (2018)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [On the Convergence and Robustness of Adversarial Training](https://mlsanity.com/paper/2112.08304/) (2021)
- [Algorithms for CVaR Optimization in MDPs](https://mlsanity.com/paper/1406.3339/) (2014)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets](https://mlsanity.com/paper/1406.1305/) (2014)
- [An Online Method for A Class of Distributionally Robust Optimization with Non-Convex Objectives](https://mlsanity.com/paper/2006.10138/) (2020)
- [Model-Based Reinforcement Learning with Adversarial Training for Online Recommendation](https://mlsanity.com/paper/1911.03845/) (2019)
- [Theoretical Analysis of Adversarial Learning: A Minimax Approach](https://mlsanity.com/paper/1811.05232/) (2018)
- [Minimax Regret Optimization for Robust Machine Learning under Distribution Shift](https://mlsanity.com/paper/2202.05436/) (2022)
- [Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits](https://mlsanity.com/paper/1401.1123/) (2014)
- [Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure](https://mlsanity.com/paper/1604.05257/) (2016)
- [On Dynamic Programming Decompositions of Static Risk Measures in Markov Decision Processes](https://mlsanity.com/paper/2304.12477/) (2023)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Principled learning method for Wasserstein distributionally robust optimization with local perturbations](https://mlsanity.com/paper/2006.03333/) (2020)
- [Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimization](https://mlsanity.com/paper/1709.02490/) (2017)
- [Oracle-Based Robust Optimization via Online Learning](https://mlsanity.com/paper/1402.6361/) (2014)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Robust Distribution Learning with Local and Global Adversarial Corruptions](https://mlsanity.com/paper/2406.06509/) (2024)
- [Online First-Order Framework for Robust Convex Optimization](https://mlsanity.com/paper/1607.06513/) (2016)
- [Data-driven Distributionally Robust Optimization over Time](https://mlsanity.com/paper/2304.05377/) (2023)
- [Wasserstein Distributionally Robust Regret Optimization](https://mlsanity.com/paper/2504.10796/) (2025)

## 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.