An Online Learning Approach for Two-Player Zero-Sum Linear Quadratic Games
Systems and Control
2026-04-06 v1 Systems and Control
Abstract
In this paper, we present an online learning approach for two-player zero-sum linear quadratic games with unknown dynamics. We develop a framework combining regularized least squares model estimation, high probability confidence sets, and surrogate model selection to maintain a regular model for policy updates. We apply a shrinkage step at each episode to identify a surrogate model in the region where the generalized algebraic Riccati equation admits a stabilizing saddle point solution. We then establish regret analysis on algorithm convergence, followed by a numerical example to illustrate the convergence performance and verify the regret analysis.
Cite
@article{arxiv.2604.02619,
title = {An Online Learning Approach for Two-Player Zero-Sum Linear Quadratic Games},
author = {Shanting Wang and Weihao Sun and Andreas A. Malikopoulos},
journal= {arXiv preprint arXiv:2604.02619},
year = {2026}
}