Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games
It addresses convergence issues in multi-agent reinforcement learning for general-sum games, offering incremental theoretical insights with a control-theoretic approach.
This paper tackles the challenge of extending reinforcement learning to multi-agent general-sum Markov games by analyzing the convergence of Stackelberg Q-value iteration, establishing finite-time error bounds for Q-functions and providing the first such guarantees for this setting.
Reinforcement learning has been successful both empirically and theoretically in single-agent settings, but extending these results to multi-agent reinforcement learning in general-sum Markov games remains challenging. This paper studies the convergence of Stackelberg Q-value iteration in two-player general-sum Markov games from a control-theoretic perspective. We introduce a relaxed policy condition tailored to the Stackelberg setting and model the learning dynamics as a switching system. By constructing upper and lower comparison systems, we establish finite-time error bounds for the Q-functions and characterize their convergence properties. Our results provide a novel control-theoretic perspective on Stackelberg learning. Moreover, to the best of the authors' knowledge, this paper offers the first finite-time convergence guarantees for Q-value iteration in general-sum Markov games under Stackelberg interactions.