# Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits

arXiv: https://arxiv.org/abs/2309.08748 · HTML: https://mlsanity.com/paper/2309.08748/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 18 of 18)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning](https://mlsanity.com/paper/2002.10790/) (2020)
- [Improved Sample Complexity Bounds for Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2303.02783/) (2023)
- [Residual Weighted Learning for Estimating Individualized Treatment Rules](https://mlsanity.com/paper/1508.03179/) (2015)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2202.09667/) (2022)
- [An explicit analysis of the entropic penalty in linear programming](https://mlsanity.com/paper/1806.01879/) (2018)
- [Thinking Inside the Ball: Near-Optimal Minimization of the Maximal Loss](https://mlsanity.com/paper/2105.01778/) (2021)
- [Semi-supervised Learning based on Distributionally Robust Optimization](https://mlsanity.com/paper/1702.08848/) (2017)
- [Regularization for Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2205.08826/) (2022)

## Built on by (most cited first, 10 of 10)

- [Distributionally Robust Off-Dynamics Reinforcement Learning: Provable Efficiency with Linear Function Approximation](https://mlsanity.com/paper/2402.15399/) (2024)
- [Minimax Optimal and Computationally Efficient Algorithms for Distributionally Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2403.09621/) (2024)
- [Upper and Lower Bounds for Distributionally Robust Off-Dynamics Reinforcement Learning](https://mlsanity.com/paper/2409.20521/) (2024)
- [Offline-to-online hyperparameter transfer for stochastic bandits](https://mlsanity.com/paper/2501.02926/) (2025)
- [Online Bayesian Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2509.14077/) (2025)
- [Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2512.12550/) (2025)
- [Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanisms](https://mlsanity.com/paper/2508.02812/) (2025)
- [Wasserstein Policy Learning for Distributional Outcomes](https://mlsanity.com/paper/2606.19117/) (2026)
- [Policy Gradient Learning for Distributionally Robust Markov Decision Processes under Wasserstein Ambiguity](https://mlsanity.com/paper/2606.27610/) (2026)
- [OTROPE: Optimal Transport-based Robust Off-policy Evaluation for Large Language Models](https://mlsanity.com/paper/2609.36264/) (2026)

## Abstract (arXiv)

Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs from the environment in which the learned policy is applied. To account for the effect of different environments during learning and execution, distributionally robust optimization (DRO) methods have been developed that compute worst-case bounds on the policy values assuming that the distribution of the new environment lies within an uncertainty set. Typically, this uncertainty set is defined based on the KL divergence around the empirical distribution computed from the logging dataset. However, the KL uncertainty set fails to encompass distributions with varying support and lacks awareness of the geometry of the distribution support. As a result, KL approaches fall short in addressing practical environment mismatches and lead to over-fitting to worst-case scenarios. To overcome these limitations, we propose a novel DRO approach that employs the Wasserstein distance instead. While Wasserstein DRO is generally computationally more expensive compared to KL DRO, we present a regularized method and a practical (biased) stochastic gradient descent method to optimize the policy efficiently. We also provide a theoretical analysis of the finite sample complexity and iteration complexity for our proposed method. We further validate our approach using a public dataset that was recorded in a randomized stoke trial.