Unsynchronized Decentralized Q-Learning: Two Timescale Analysis By Persistence

TL;DR

This paper analyzes an unsynchronized decentralized Q-learning algorithm in multi-agent reinforcement learning, demonstrating it can converge to equilibrium without the need for synchronized policy updates, thus broadening its practical applicability.

Contribution

It introduces a high-probability convergence analysis for an unsynchronized variant of decentralized Q-learning using constant learning rates, relaxing previous synchronization assumptions.

Findings

Convergence to equilibrium under high probability

Constant learning rates are critical for analysis

Applicable to a range of decentralized algorithms

Abstract

Non-stationarity is a fundamental challenge in multi-agent reinforcement learning (MARL), where agents update their behaviour as they learn. Many theoretical advances in MARL avoid the challenge of non-stationarity by coordinating the policy updates of agents in various ways, including synchronizing times at which agents are allowed to revise their policies. Synchronization enables analysis of many MARL algorithms via multi-timescale methods, but such synchronization is infeasible in many decentralized applications. In this paper, we study an unsynchronized variant of the decentralized Q-learning algorithm, a recent MARL algorithm for stochastic games. We provide sufficient conditions under which the unsynchronized algorithm drives play to equilibrium with high probability. Our solution utilizes constant learning rates in the Q-factor update, which we show to be critical for relaxing the synchronization assumptions of earlier work. Our analysis also applies to unsynchronized generalizations of a number of other algorithms from the regret testing tradition, whose performance is analyzed by multi-timescale methods that study Markov chains obtained via policy update dynamics. This work extends the applicability of the decentralized Q-learning algorithm and its relatives to settings in which parameters are selected in an independent manner, and tames non-stationarity without imposing the coordination assumptions of prior work.