{"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/near-optimal-pure-exploration-in-matrix-games","title":"Near-Optimal Pure Exploration in Matrix Games: A Generalization of Stochastic Bandits & Dueling Bandits","arxiv_id":"2310.16252","date":"2023-10-25","proceeding":null,"authors":["Arnab Maiti","Ross Boczar","Kevin Jamieson","Lillian J. Ratliff"],"abstract":"We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input matrix $A\\in[-1,1]^{n\\times m}$ and observe $A_{i,j}+\\eta$ where $\\eta$ is a zero-mean 1-sub-Gaussian noise. The aim of the learner is to identify the PSNE of $A$, whenever it exists, with high probability while taking as few samples as possible. Zhou et al. (2017) presents an instance-dependent sample complexity lower bound that depends only on the entries in the row and column in which the PSNE lies. We design a near-optimal algorithm whose sample complexity matches the lower bound, up to log factors. The problem of identifying the PSNE also generalizes the problem of pure exploration in stochastic multi-armed bandits and dueling bandits, and our result matches the optimal bounds, up to log factors, in both the settings.","url_abs":"https://arxiv.org/abs/2310.16252v2","url_pdf":"https://arxiv.org/pdf/2310.16252v2.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":"near-optimal-pure-exploration-in-matrix-games","repo_url":"https://github.com/aistats2024-noisy-psne/midsearch","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","reach":null}],"tasks":[{"task_slug":"multi-armed-bandits","task_name":"Multi-Armed Bandits"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}