Sample-Efficient Regret-Minimizing Double Oracle in Extensive-Form Games

Fuente: arXiv
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Main Authors: Tang, Xiaohang, Wang, Chiyuan, Ma, Chengdong, Bogunovic, Ilija, McAleer, Stephen, Yang, Yaodong
Format: Preprint
Published: 2024
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author Tang, Xiaohang
Wang, Chiyuan
Ma, Chengdong
Bogunovic, Ilija
McAleer, Stephen
Yang, Yaodong
author_facet Tang, Xiaohang
Wang, Chiyuan
Ma, Chengdong
Bogunovic, Ilija
McAleer, Stephen
Yang, Yaodong
contents Extensive-Form Game (EFG) represents a fundamental model for analyzing sequential interactions among multiple agents and the primary challenge to solve it lies in mitigating sample complexity. Existing research indicated that Double Oracle (DO) can reduce the sample complexity dependence on the information set number $|S|$ to the final restricted game size $X$ in solving EFG. This is attributed to the early convergence of full-game Nash Equilibrium (NE) through iteratively solving restricted games. However, we prove that the state-of-the-art Extensive-Form Double Oracle (XDO) exhibits \textit{exponential} sample complexity of $X$, due to its exponentially increasing restricted game expansion frequency. Here we introduce Adaptive Double Oracle (AdaDO) to significantly alleviate sample complexity to \textit{polynomial} by deploying the optimal expansion frequency. Furthermore, to comprehensively study the principles and influencing factors underlying sample complexity, we introduce a novel theoretical framework Regret-Minimizing Double Oracle (RMDO) to provide directions for designing efficient DO algorithms. Empirical results demonstrate that AdaDO attains the more superior approximation of NE with less sample complexity than the strong baselines including Linear CFR, MCCFR and existing DO. Importantly, combining RMDO with warm starting and stochastic regret minimization further improves convergence rate and scalability, thereby paving the way for addressing complex multi-agent tasks.
format Preprint
id arxiv_https___arxiv_org_abs_2411_00954
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Sample-Efficient Regret-Minimizing Double Oracle in Extensive-Form Games
Tang, Xiaohang
Wang, Chiyuan
Ma, Chengdong
Bogunovic, Ilija
McAleer, Stephen
Yang, Yaodong
Computer Science and Game Theory
Extensive-Form Game (EFG) represents a fundamental model for analyzing sequential interactions among multiple agents and the primary challenge to solve it lies in mitigating sample complexity. Existing research indicated that Double Oracle (DO) can reduce the sample complexity dependence on the information set number $|S|$ to the final restricted game size $X$ in solving EFG. This is attributed to the early convergence of full-game Nash Equilibrium (NE) through iteratively solving restricted games. However, we prove that the state-of-the-art Extensive-Form Double Oracle (XDO) exhibits \textit{exponential} sample complexity of $X$, due to its exponentially increasing restricted game expansion frequency. Here we introduce Adaptive Double Oracle (AdaDO) to significantly alleviate sample complexity to \textit{polynomial} by deploying the optimal expansion frequency. Furthermore, to comprehensively study the principles and influencing factors underlying sample complexity, we introduce a novel theoretical framework Regret-Minimizing Double Oracle (RMDO) to provide directions for designing efficient DO algorithms. Empirical results demonstrate that AdaDO attains the more superior approximation of NE with less sample complexity than the strong baselines including Linear CFR, MCCFR and existing DO. Importantly, combining RMDO with warm starting and stochastic regret minimization further improves convergence rate and scalability, thereby paving the way for addressing complex multi-agent tasks.
title Sample-Efficient Regret-Minimizing Double Oracle in Extensive-Form Games
topic Computer Science and Game Theory
url https://arxiv.org/abs/2411.00954