Generalized Bandit Regret Minimizer Framework in Imperfect Information Extensive-Form Game
This work addresses a core challenge in game theory and reinforcement learning for AI agents, offering a modular and computationally efficient solution with significant theoretical improvements.
The paper tackles the problem of learning approximate Nash equilibrium in two-player zero-sum imperfect information extensive-form games under bandit feedback, proposing a generalized framework and a novel method called SIX-OMD that improves the convergence rate from O(√(XB/T) + √(YC/T)) to O(√(M_X/T) + √(M_Y/T)).
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 $\ell^t$ 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 $O(\sqrt{X B/T}+\sqrt{Y C/T})$ to $O(\sqrt{ M_{\mathcal{X}}/T} +\sqrt{ M_{\mathcal{Y}}/T})$. Moreover, SIX-OMD is computationally efficient as it needs to perform the current strategy and average strategy updates only along the sampled trajectory.