# Distributional robustness in minimax linear quadratic control with Wasserstein distance

arXiv: https://arxiv.org/abs/2102.12715 · HTML: https://mlsanity.com/paper/2102.12715/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2021.

## Built on by (most cited first, 7 of 7)

- [A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distance](https://mlsanity.com/paper/2304.06783/) (2023)
- [Policy Evaluation in Distributional LQR](https://mlsanity.com/paper/2303.13657/) (2023)
- [Learning Optimal Distributionally Robust Stochastic Control in Continuous State Spaces](https://mlsanity.com/paper/2406.11281/) (2024)
- [Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning](https://mlsanity.com/paper/2510.10214/) (2025)
- [Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets](https://mlsanity.com/paper/2512.10906/) (2025)
- [Data-driven robust Markov decision processes on Borel spaces: performance guarantees via an axiomatic approach](https://mlsanity.com/paper/2603.08979/) (2026)
- [Policy Gradient Learning for Distributionally Robust Markov Decision Processes under Wasserstein Ambiguity](https://mlsanity.com/paper/2606.27610/) (2026)

## Abstract (arXiv)

To address the issue of inaccurate distributions in practical stochastic systems, a minimax linear-quadratic control method is proposed using the Wasserstein metric. Our method aims to construct a control policy that is robust against errors in an empirical distribution of underlying uncertainty, by adopting an adversary that selects the worst-case distribution. The opponent receives a Wasserstein penalty proportional to the amount of deviation from the empirical distribution. A closed-form expression of the finite-horizon optimal policy pair is derived using a Riccati equation. The result is then extended to the infinite-horizon average cost setting by identifying conditions under which the Riccati recursion converges to the unique positive semi-definite solution to an algebraic Riccati equation. Our method is shown to possess several salient features including closed-loop stability, and an out-of-sample performance guarantee. We also discuss how to optimize the penalty parameter for enhancing the distributional robustness of our control policy. Last but not least, a theoretical connection to the classical H_∞-method is identified from the perspective of distributional robustness.