Kernel Conditional Moment Constraints for Confounding Robust Inference

TL;DR

This paper introduces a kernel-based estimator for policy evaluation under unobserved confounding in offline contextual bandits, providing sharper bounds and extending sensitivity models with theoretical guarantees.

Contribution

It proposes a novel kernel conditional moment constraint approach that improves policy value bounds and extends classical sensitivity models with theoretical and empirical validation.

Findings

Provides a sharp lower bound estimator for policy value.

Extends sensitivity analysis using f-divergence.

Demonstrates effectiveness on synthetic and real data.

Abstract

We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However, existing work often resorts to some coarse relaxation of the uncertainty set for the sake of tractability, leading to overly conservative estimation of the policy value. In this paper, we propose a general estimator that provides a sharp lower bound of the policy value. It can be shown that our estimator contains the recently proposed sharp estimator by Dorn and Guo (2022) as a special case, and our method enables a novel extension of the classical marginal sensitivity model using f-divergence. To construct our estimator, we leverage the kernel method to obtain a tractable approximation to the conditional moment constraints, which traditional non-sharp estimators failed to take into account. In the theoretical analysis, we provide a condition for the choice of the kernel which guarantees no specification error that biases the lower bound estimation. Furthermore, we provide consistency guarantees of policy evaluation and learning. In the experiments with synthetic and real-world data, we demonstrate the effectiveness of the proposed method.