Optimal Estimation of Off-Policy Policy Gradient via Double Fitted Iteration
This addresses a key problem in reinforcement learning for scenarios where direct sampling from the target policy is not possible, offering a more efficient and accurate estimation method.
The paper tackles the challenge of off-policy policy gradient estimation, where only data from an unknown behavior policy is available, by proposing the double Fitted PG algorithm, which achieves a tight finite-sample error bound and statistically optimal asymptotic normality, outperforming existing methods in experiments.
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.