Generalized Bandit Regret Minimizer Framework in Imperfect Information Extensive-Form Game

Abstract

Regret minimization methods are a powerful tool for learning approximate Nash equilibrium (NE) in two-player zero-sum imperfect information extensive-form games (IIEGs). We consider the problem in the interactive bandit-feedback setting where we don't know the dynamics of the IIEG. In general, only the interactive trajectory and the reached terminal node value v(z^t) are revealed. To learn NE, the regret minimizer is required to estimate the full-feedback loss gradient ^t by v(z^t) and minimize the regret. In this paper, we propose a generalized framework for this learning setting. It presents a theoretical framework for the design and the modular analysis of the bandit regret minimization methods. We demonstrate that the most recent bandit regret minimization methods can be analyzed as a particular case of our framework. Following this framework, we describe a novel method SIX-OMD to learn approximate NE. It is model-free and extremely improves the best existing convergence rate from the order of O(X B/T+Y C/T) to O( M_X/T + M_Y/T). Moreover, SIX-OMD is computationally efficient as it needs to perform the current strategy and average strategy updates only along the sampled trajectory.

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Reproductions