Optimal Estimation of Off-Policy Policy Gradient via Double Fitted Iteration

TL;DR

This paper introduces the double Fitted Policy Gradient (FPG) algorithm for off-policy policy gradient estimation, achieving optimal statistical properties and outperforming existing methods in various settings.

Contribution

The paper proposes a novel FPG algorithm that works with arbitrary policy parameterizations and provides tight finite-sample bounds and asymptotic normality results.

Findings

FPG achieves statistically optimal estimation error matching the Cramer-Rao bound.

FPG outperforms existing importance sampling and variance reduction methods.

Empirical results show significant improvements in policy estimation and optimization tasks.

Abstract

Policy gradient (PG) estimation becomes a challenge when we are not allowed to sample with the target policy but only have access to a dataset generated by some unknown behavior policy. Conventional methods for off-policy PG estimation often suffer from either significant bias or exponentially large variance. In this paper, we propose the double Fitted PG estimation (FPG) algorithm. FPG can work with an arbitrary policy parameterization, assuming access to a Bellman-complete value function class. In the case of linear value function approximation, we provide a tight finite-sample upper bound on policy gradient estimation error, that is governed by the amount of distribution mismatch measured in feature space. We also establish the asymptotic normality of FPG estimation error with a precise covariance characterization, which is further shown to be statistically optimal with a matching Cramer-Rao lower bound. Empirically, we evaluate the performance of FPG on both policy gradient estimation and policy optimization, using either softmax tabular or ReLU policy networks. Under various metrics, our results show that FPG significantly outperforms existing off-policy PG estimation methods based on importance sampling and variance reduction techniques.