A finite time analysis of distributed Q-learning

TL;DR

This paper provides a finite-time analysis and new sample complexity bounds for distributed Q-learning in multi-agent reinforcement learning, demonstrating how multiple agents can cooperatively learn optimal policies without centralized reward access.

Contribution

It introduces a finite-time analysis for distributed Q-learning and derives novel sample complexity bounds under tabular settings, advancing theoretical understanding of multi-agent RL algorithms.

Findings

New sample complexity bounds for distributed Q-learning

Finite-time convergence guarantees in multi-agent settings

Analysis under tabular lookup with cooperative agents

Abstract

Multi-agent reinforcement learning (MARL) has witnessed a remarkable surge in interest, fueled by the empirical success achieved in applications of single-agent reinforcement learning (RL). In this study, we consider a distributed Q-learning scenario, wherein a number of agents cooperatively solve a sequential decision making problem without access to the central reward function which is an average of the local rewards. In particular, we study finite-time analysis of a distributed Q-learning algorithm, and provide a new sample complexity result of $\tilde{\mathcal{O}}\left( \min\left\{\frac{1}{\epsilon^2}\frac{t_{\text{mix}}}{(1-\gamma)^6 d_{\min}^4 } ,\frac{1}{\epsilon}\frac{\sqrt{|\gS||\gA|}}{(1-\sigma_2(\boldsymbol{W}))(1-\gamma)^4 d_{\min}^3} \right\}\right)$ under tabular lookup