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

arXiv: https://arxiv.org/abs/2209.15141 · HTML: https://mlsanity.com/paper/2209.15141/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [Learning and Planning in Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2006.16318/) (2020)
- [Average-Reward Learning and Planning with Options](https://mlsanity.com/paper/2110.13855/) (2021)

## Built on by (most cited first, 6 of 6)

- [Model-Free Robust Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2305.10504/) (2023)
- [RVI-SAC: Average Reward Off-Policy Deep Reinforcement Learning](https://mlsanity.com/paper/2408.01972/) (2024)
- [Model-Free Robust Average-Reward Reinforcement Learning with Sample Complexity Analysis](https://mlsanity.com/paper/2505.12462/) (2025)
- [Position: Deployed Reinforcement Learning should be Continual](https://mlsanity.com/paper/2606.04029/) (2026)
- [Average Reward Reinforcement Learning for Omega-Regular and Mean-Payoff Objectives](https://mlsanity.com/paper/2505.15693/) (2025)
- [Vector Bellman Theory for Multichain Robust Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2609.28792/) (2026)

## Abstract (arXiv)

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.