Optimal Non-Asymptotic Rates of Value Iteration for Average-Reward Markov Decision Processes
Jongmin Lee Ernest K. Ryu
While there is an extensive body of research on the analysis of Value Iteration (VI) for discounted cumulative-reward MDPs, prior work on analyzing VI for (undiscounted) average-reward MDPs has been limited, and most prior results focus on asymptotic rates in terms of Bellman error. In this work, we conduct refined non-asymptotic analyses of average-reward MDPs, obtaining a collection of convergence results advancing our understanding of the setup. Among our new results, most notable are the $\mathcal{O}(1/k)$-rates of Anchored Value Iteration on the Bellman error under the multichain setup and the span-based complexity lower bound that matches the $\mathcal{O}(1/k)$ upper bound up to a constant factor of $8$ in the weakly communicating and unichain setups.
Average-reward Markov decision process, Average-reward MDP, Value iteration, Reinforcement learning theory, RL theroy, Dynamic programming, Convergence analysis, Anchoring mechanism
We characterize optimal non-asymptotic convergence rates of VI and its variants in average-reward MDPs.