Learning bounds for doubly-robust covariate shift adaptation

• URL: http://arxiv.org/abs/2511.11003v1
• Date: Fri, 14 Nov 2025 06:46:23 GMT
• Title: Learning bounds for doubly-robust covariate shift adaptation
• Authors: Jeonghwan Lee, Cong Ma,
• Abstract summary: Distribution shift between the training domain and the test domain poses a key challenge for machine learning.<n> doubly-robust (DR) estimator combines density ratio estimation with a pilot regression model.<n>This paper establishes the first non-asymptotic learning bounds for the DR estimator.
• Score: 8.24901041136559
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Distribution shift between the training domain and the test domain poses a key challenge for modern machine learning. An extensively studied instance is the \emph{covariate shift}, where the marginal distribution of covariates differs across domains, while the conditional distribution of outcome remains the same. The doubly-robust (DR) estimator, recently introduced by \cite{kato2023double}, combines the density ratio estimation with a pilot regression model and demonstrates asymptotic normality and $\sqrt{n}$-consistency, even when the pilot estimates converge slowly. However, the prior arts has focused exclusively on deriving asymptotic results and has left open the question of non-asymptotic guarantees for the DR estimator. This paper establishes the first non-asymptotic learning bounds for the DR covariate shift adaptation. Our main contributions are two-fold: (\romannumeral 1) We establish \emph{structure-agnostic} high-probability upper bounds on the excess target risk of the DR estimator that depend only on the $L^2$-errors of the pilot estimates and the Rademacher complexity of the model class, without assuming specific procedures to obtain the pilot estimate, and (\romannumeral 2) under \emph{well-specified parameterized models}, we analyze the DR covariate shift adaptation based on modern techniques for non-asymptotic analysis of MLE, whose key terms governed by the Fisher information mismatch term between the source and target distributions. Together, these findings bridge asymptotic efficiency properties and a finite-sample out-of-distribution generalization bounds, providing a comprehensive theoretical underpinnings for the DR covariate shift adaptation.

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