{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-zero-sum-linear-quadratic-games-with","title":"Learning Zero-Sum Linear Quadratic Games with Improved Sample Complexity and Last-Iterate Convergence","arxiv_id":"2309.04272","date":"2023-09-08","proceeding":null,"authors":["Jiduan Wu","Anas Barakat","Ilyas Fatkhullin","Niao He"],"abstract":"Zero-sum Linear Quadratic (LQ) games are fundamental in optimal control and can be used (i)~as a dynamic game formulation for risk-sensitive or robust control and (ii)~as a benchmark setting for multi-agent reinforcement learning with two competing agents in continuous state-control spaces. In contrast to the well-studied single-agent linear quadratic regulator problem, zero-sum LQ games entail solving a challenging nonconvex-nonconcave min-max problem with an objective function that lacks coercivity. Recently, Zhang et al. showed that an~$\\epsilon$-Nash equilibrium (NE) of finite horizon zero-sum LQ games can be learned via nested model-free Natural Policy Gradient (NPG) algorithms with poly$(1/\\epsilon)$ sample complexity. In this work, we propose a simpler nested Zeroth-Order (ZO) algorithm improving sample complexity by several orders of magnitude and guaranteeing convergence of the last iterate. Our main results are two-fold: (i) in the deterministic setting, we establish the first global last-iterate linear convergence result for the nested algorithm that seeks NE of zero-sum LQ games; (ii) in the model-free setting, we establish a~$\\widetilde{\\mathcal{O}}(\\epsilon^{-2})$ sample complexity using a single-point ZO estimator. For our last-iterate convergence results, our analysis leverages the Implicit Regularization (IR) property and a new gradient domination condition for the primal function. Our key improvements in the sample complexity rely on a more sample-efficient nested algorithm design and a finer control of the ZO natural gradient estimation error utilizing the structure endowed by the finite-horizon setting.","url_abs":"https://arxiv.org/abs/2309.04272v3","url_pdf":"https://arxiv.org/pdf/2309.04272v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-zero-sum-linear-quadratic-games-with","repo_url":"https://github.com/wujiduan/zero-sum-lq-games","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"multi-agent-reinforcement-learning","task_name":"Multi-agent Reinforcement Learning"},{"task_slug":"policy-gradient-methods","task_name":"Policy Gradient Methods"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}