Robust PAC Learning of Concurrent Stochastic Games

2026-09-03

AI Summary

该研究提出了一种针对存在转换不确定性的并发随机博弈的PAC学习框架，通过构建数据驱动的信心集和采用鲁棒MDP探索机制来寻找社会福利最优的近似纳什均衡。

Abstract

We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.

Problem

• Concurrent Stochastic Games
• PAC Learning
• Nash Equilibrium
• Transition Uncertainty

Innovation

• Probably Approximately Correct (PAC) Learning
• Concurrent Stochastic Games (CSGs)
• Nash Margin Characterisation
• Robust MDP-based Exploration