{"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/adapting-to-game-trees-in-zero-sum-imperfect","title":"Adapting to game trees in zero-sum imperfect information games","arxiv_id":"2212.12567","date":"2022-12-23","proceeding":null,"authors":["Côme Fiegel","Pierre Ménard","Tadashi Kozuno","Rémi Munos","Vianney Perchet","Michal Valko"],"abstract":"Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\\widetilde{\\mathcal{O}}(H(A_{\\mathcal{X}}+B_{\\mathcal{Y}})/\\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\\mathcal{X}}$ and $B_{\\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regularized leader (FTRL) algorithms for this setting: Balanced FTRL which matches this lower bound, but requires the knowledge of the information set structure beforehand to define the regularization; and Adaptive FTRL which needs $\\widetilde{\\mathcal{O}}(H^2(A_{\\mathcal{X}}+B_{\\mathcal{Y}})/\\epsilon^2)$ realizations without this requirement by progressively adapting the regularization to the observations.","url_abs":"https://arxiv.org/abs/2212.12567v2","url_pdf":"https://arxiv.org/pdf/2212.12567v2.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":"adapting-to-game-trees-in-zero-sum-imperfect","repo_url":"https://github.com/anon17893/iig-tree-adaptation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2212.12567","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}