Off-Policy Evaluation via the Regularized Lagrangian

TL;DR

This paper unifies various off-policy evaluation estimators under a common framework using regularized Lagrangians, leading to new estimators with improved performance and better bias-variance tradeoffs.

Contribution

It introduces a unified formulation of DICE estimators as regularized Lagrangians, enabling the development of new estimators with enhanced stability and accuracy.

Findings

Dual solutions improve the bias-variance tradeoff.

New estimators outperform existing methods in empirical tests.

Unified framework facilitates exploration of estimator space.

Abstract

The recently proposed distribution correction estimation (DICE) family of estimators has advanced the state of the art in off-policy evaluation from behavior-agnostic data. While these estimators all perform some form of stationary distribution correction, they arise from different derivations and objective functions. In this paper, we unify these estimators as regularized Lagrangians of the same linear program. The unification allows us to expand the space of DICE estimators to new alternatives that demonstrate improved performance. More importantly, by analyzing the expanded space of estimators both mathematically and empirically we find that dual solutions offer greater flexibility in navigating the tradeoff between optimization stability and estimation bias, and generally provide superior estimates in practice.