Scaling Marginalized Importance Sampling to High-Dimensional State-Spaces via State Abstraction

TL;DR

This paper introduces a method to improve off-policy evaluation in high-dimensional reinforcement learning by using state abstraction to reduce variance and enhance accuracy of importance sampling estimators.

Contribution

It proposes a novel approach that leverages state abstraction to lower the variance of importance sampling ratios, improving OPE accuracy in high-dimensional spaces.

Findings

Lower variance in abstract ratios leads to reduced mean-squared error.

Abstract ratios improve robustness to hyperparameter tuning.

Method outperforms existing techniques on high-dimensional tasks.

Abstract

We consider the problem of off-policy evaluation (OPE) in reinforcement learning (RL), where the goal is to estimate the performance of an evaluation policy, $\pi_e$, using a fixed dataset, $\mathcal{D}$, collected by one or more policies that may be different from $\pi_e$. Current OPE algorithms may produce poor OPE estimates under policy distribution shift i.e., when the probability of a particular state-action pair occurring under $\pi_e$ is very different from the probability of that same pair occurring in $\mathcal{D}$ (Voloshin et al. 2021, Fu et al. 2021). In this work, we propose to improve the accuracy of OPE estimators by projecting the high-dimensional state-space into a low-dimensional state-space using concepts from the state abstraction literature. Specifically, we consider marginalized importance sampling (MIS) OPE algorithms which compute state-action distribution correction ratios to produce their OPE estimate. In the original ground state-space, these ratios may have high variance which may lead to high variance OPE. However, we prove that in the lower-dimensional abstract state-space the ratios can have lower variance resulting in lower variance OPE. We then highlight the challenges that arise when estimating the abstract ratios from data, identify sufficient conditions to overcome these issues, and present a minimax optimization problem whose solution yields these abstract ratios. Finally, our empirical evaluation on difficult, high-dimensional state-space OPE tasks shows that the abstract ratios can make MIS OPE estimators achieve lower mean-squared error and more robust to hyperparameter tuning than the ground ratios.