Learning Infinite-horizon Average-reward MDPs with Linear Function Approximation

TL;DR

This paper introduces new algorithms for learning infinite-horizon average-reward MDPs with linear function approximation, achieving near-optimal regret bounds and improving upon previous results in sample complexity and regret.

Contribution

It presents both computationally efficient and inefficient algorithms with improved regret bounds, and connects these algorithms to existing policy gradient methods.

Findings

Achieved $ ilde{O}( oot{T}{} )$ regret with some algorithms.

Developed an efficient algorithm with $ ilde{O}(T^{3/4})$ regret.

Improved the regret bound over previous work by Hao et al. (2020).

Abstract

We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we first propose a computationally inefficient algorithm with optimal $\widetilde{O}(\sqrt{T})$ regret and another computationally efficient variant with $\widetilde{O}(T^{3/4})$ regret, where $T$ is the number of interactions. Next, taking inspiration from adversarial linear bandits, we develop yet another efficient algorithm with $\widetilde{O}(\sqrt{T})$ regret under a different set of assumptions, improving the best existing result by Hao et al. (2020) with $\widetilde{O}(T^{2/3})$ regret. Moreover, we draw a connection between this algorithm and the Natural Policy Gradient algorithm proposed by Kakade (2002), and show that our analysis improves the sample complexity bound recently given by Agarwal et al. (2020).