Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games

TL;DR

This paper provides the first finite-time convergence guarantees for Q-value iteration in general-sum Markov games with Stackelberg interactions, using a control-theoretic approach.

Contribution

It introduces a novel control-theoretic framework and relaxed policy conditions for analyzing Stackelberg Q-learning in multi-agent settings.

Findings

Established finite-time error bounds for Stackelberg Q-functions.

Characterized convergence properties of the learning dynamics.

Provided the first finite-time guarantees for Q-value iteration in this context.

Abstract

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.