Combining Experimental and Historical Data for Policy Evaluation

TL;DR

This paper introduces new methods for policy evaluation that combine experimental and historical data sources, optimizing for minimal mean square error and robustness, with theoretical guarantees and practical validation.

Contribution

It proposes novel data integration techniques that linearly combine estimators from experimental and historical data, with optimized weights and robustness features, extending to sequential decision making.

Findings

Proposed estimators outperform existing methods in simulations.

Theoretical error bounds and robustness properties are established.

Real-data experiments demonstrate superior performance.

Abstract

This paper studies policy evaluation with multiple data sources, especially in scenarios that involve one experimental dataset with two arms, complemented by a historical dataset generated under a single control arm. We propose novel data integration methods that linearly integrate base policy value estimators constructed based on the experimental and historical data, with weights optimized to minimize the mean square error (MSE) of the resulting combined estimator. We further apply the pessimistic principle to obtain more robust estimators, and extend these developments to sequential decision making. Theoretically, we establish non-asymptotic error bounds for the MSEs of our proposed estimators, and derive their oracle, efficiency and robustness properties across a broad spectrum of reward shift scenarios. Numerical experiments and real-data-based analyses from a ridesharing company demonstrate the superior performance of the proposed estimators.