Episodic Logit-Q Dynamics for Efficient Learning in Stochastic Teams

TL;DR

This paper introduces a novel learning dynamics combining log-linear learning and value iteration for stochastic games, achieving efficient equilibrium convergence without requiring agents to seek equilibrium actively.

Contribution

It proposes a new independent learning dynamics that guarantees convergence to the optimal equilibrium in stochastic games, addressing non-stationarity and practical implementation issues.

Findings

Proves convergence to efficient equilibrium in stochastic games.

Demonstrates practical applicability in autonomous systems.

Addresses non-stationarity through episodic Q-function updates.

Abstract

We present new learning dynamics combining (independent) log-linear learning and value iteration for stochastic games within the auxiliary stage game framework. The dynamics presented provably attain the efficient equilibrium (also known as optimal equilibrium) in identical-interest stochastic games, beyond the recent concentration of progress on provable convergence to some (possibly inefficient) equilibrium. The dynamics are also independent in the sense that agents take actions consistent with their local viewpoint to a reasonable extent rather than seeking equilibrium. These aspects can be of practical interest in the control applications of intelligent and autonomous systems. The key challenges are the convergence to an inefficient equilibrium and the non-stationarity of the environment from a single agent's viewpoint due to the adaptation of others. The log-linear update plays an important role in addressing the former. We address the latter through the play-in-episodes scheme in which the agents update their Q-function estimates only at the end of the episodes.