First-order Policy Optimization for Robust Policy Evaluation

TL;DR

This paper introduces FRPE, a unified first-order policy evaluation method for robust MDPs that achieves linear convergence deterministically and efficient sample complexity stochastically, applicable to large-scale problems.

Contribution

It develops the first unified framework for robust policy evaluation applicable to both deterministic and stochastic settings with various representations.

Findings

Linear convergence in deterministic setting

Sample complexity of (1/^2) in stochastic setting

Extension to evaluating robust state-action value functions

Abstract

We adopt a policy optimization viewpoint towards policy evaluation for robust Markov decision process with $\mathrm{s}$-rectangular ambiguity sets. The developed method, named first-order policy evaluation (FRPE), provides the first unified framework for robust policy evaluation in both deterministic (offline) and stochastic (online) settings, with either tabular representation or generic function approximation. In particular, we establish linear convergence in the deterministic setting, and $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity in the stochastic setting. FRPE also extends naturally to evaluating the robust state-action value function with $(\mathrm{s}, \mathrm{a})$-rectangular ambiguity sets. We discuss the application of the developed results for stochastic policy optimization of large-scale robust MDPs.