On Convergence of Average-Reward Off-Policy Control Algorithms in Weakly Communicating MDPs

TL;DR

This paper proves the convergence of two average-reward off-policy control algorithms in the broad class of weakly communicating MDPs, extending their applicability and providing the first such convergence results.

Contribution

It demonstrates the first convergence proofs for these algorithms in weakly communicating MDPs, broadening their theoretical foundation.

Findings

Differential Q-learning converges in weakly communicating MDPs.

RVI Q-learning converges in weakly communicating MDPs.

Options algorithms also converge under weakly communicating conditions.

Abstract

We show two average-reward off-policy control algorithms, Differential Q-learning (Wan, Naik, & Sutton 2021a) and RVI Q-learning (Abounadi Bertsekas & Borkar 2001), converge in weakly communicating MDPs. Weakly communicating MDPs are the most general MDPs that can be solved by a learning algorithm with a single stream of experience. The original convergence proofs of the two algorithms require that the solution set of the average-reward optimality equation only has one degree of freedom, which is not necessarily true for weakly communicating MDPs. To the best of our knowledge, our results are the first showing average-reward off-policy control algorithms converge in weakly communicating MDPs. As a direct extension, we show that average-reward options algorithms for temporal abstraction introduced by Wan, Naik, & Sutton (2021b) converge if the Semi-MDP induced by options is weakly communicating.