Distributional Off-Policy Evaluation with Deep Quantile Process Regression

TL;DR

This paper introduces DQPOPE, a novel deep quantile process regression method for off-policy evaluation that estimates the entire return distribution, offering theoretical insights and improved empirical performance.

Contribution

It presents a new distributional OPE algorithm with rigorous sample complexity analysis and extends quantile regression techniques to estimate continuous return distributions.

Findings

DQPOPE achieves statistical advantages with the same sample size as traditional methods.

Empirical results show DQPOPE provides more precise and robust policy value estimates.

Theoretical analysis extends quantile regression to continuous functions in deep neural networks.

Abstract

This paper investigates the off-policy evaluation (OPE) problem from a distributional perspective. Rather than focusing solely on the expectation of the total return, as in most existing OPE methods, we aim to estimate the entire return distribution. To this end, we introduce a quantile-based approach for OPE using deep quantile process regression, presenting a novel algorithm called Deep Quantile Process regression-based Off-Policy Evaluation (DQPOPE). We provide new theoretical insights into the deep quantile process regression technique, extending existing approaches that estimate discrete quantiles to estimate a continuous quantile function. A key contribution of our work is the rigorous sample complexity analysis for distributional OPE with deep neural networks, bridging theoretical analysis with practical algorithmic implementations. We show that DQPOPE achieves statistical advantages by estimating the full return distribution using the same sample size required to estimate a single policy value using conventional methods. Empirical studies further show that DQPOPE provides significantly more precise and robust policy value estimates than standard methods, thereby enhancing the practical applicability and effectiveness of distributional reinforcement learning approaches.