{"ID":2883591,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.07699","arxiv_id":"2508.07699","title":"Last-Iterate Convergence in Adaptive Regret Minimization for Approximate Extensive-Form Perfect Equilibrium","abstract":"The Nash Equilibrium (NE) assumes rational play in imperfect-information Extensive-Form Games (EFGs) but fails to ensure optimal strategies for off-equilibrium branches of the game tree, potentially leading to suboptimal outcomes in practical settings. To address this, the Extensive-Form Perfect Equilibrium (EFPE), a refinement of NE, introduces controlled perturbations to model potential player errors. However, existing EFPE-finding algorithms, which typically rely on average strategy convergence and fixed perturbations, face significant limitations: computing average strategies incurs high computational costs and approximation errors, while fixed perturbations create a trade-off between NE approximation accuracy and the convergence rate of NE refinements. To tackle these challenges, we propose an efficient adaptive regret minimization algorithm for computing approximate EFPE, achieving last-iterate convergence in two-player zero-sum EFGs. Our approach introduces Reward Transformation Counterfactual Regret Minimization (RTCFR) to solve perturbed games and defines a novel metric, the Information Set Nash Equilibrium (ISNE), to dynamically adjust perturbations. Theoretical analysis confirms convergence to EFPE, and experimental results demonstrate that our method significantly outperforms state-of-the-art algorithms in both NE and EFPE-finding tasks.","short_abstract":"The Nash Equilibrium (NE) assumes rational play in imperfect-information Extensive-Form Games (EFGs) but fails to ensure optimal strategies for off-equilibrium branches of the game tree, potentially leading to suboptimal outcomes in practical settings. To address this, the Extensive-Form Perfect Equilibrium (EFPE), a r...","url_abs":"https://arxiv.org/abs/2508.07699","url_pdf":"https://arxiv.org/pdf/2508.07699v1","authors":"[\"Hang Ren\",\"Xiaozhen Sun\",\"Tianzi Ma\",\"Jiajia Zhang\",\"Xuan Wang\"]","published":"2025-08-11T07:22:54Z","proceeding":"cs.GT","tasks":"[\"cs.GT\"]","methods":"[]","has_code":false}