# Minimax Q-learning Control for Linear Systems Using the Wasserstein Metric

arXiv: https://arxiv.org/abs/2010.06794 · HTML: https://mlsanity.com/paper/2010.06794/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [DR-PETS: Learning-Based Control With Planning in Adversarial Environments](https://mlsanity.com/paper/2503.20660/) (2025)
- [Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning](https://mlsanity.com/paper/2510.10214/) (2025)

## Abstract (arXiv)

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear systems and adopt a Wasserstein penalty to address the distribution uncertainty of additive stochastic disturbances. By constructing an equivalent deterministic game of the penalized LQR problem, we propose a Q-learning method with convergence guarantees to learn an optimal minimax controller.