Inexact GMRES Policy Iteration for Large-Scale Markov Decision Processes

TL;DR

This paper introduces inexact GMRES policy iteration, a novel method for large-scale Markov decision processes that improves computational efficiency while maintaining convergence guarantees.

Contribution

It proposes inexact policy iteration inspired by semismooth Newton methods and designs a GMRES-based approximation for large-scale MDPs.

Findings

Achieves significant speedups over traditional policy iteration.

Demonstrates practical efficiency on an MDP with 10,000 states.

Maintains local contraction guarantees.

Abstract

Policy iteration enjoys a local quadratic rate of contraction, but its iterations are computationally expensive for Markov decision processes (MDPs) with a large number of states. In light of the connection between policy iteration and the semismooth Newton method and taking inspiration from the inexact variants of the latter, we propose \textit{inexact policy iteration}, a new class of methods for large-scale finite MDPs with local contraction guarantees. We then design an instance based on the deployment of GMRES for the approximate policy evaluation step, which we call inexact GMRES policy iteration. Finally, we demonstrate the superior practical performance of inexact GMRES policy iteration on an MDP with 10000 states, where it achieves a $\times 5.8$ and $\times 2.2$ speedup with respect to policy iteration and optimistic policy iteration, respectively.