A Minimax Theory of Nonparametric Regression Under Covariate Shift
Abstract
We consider nonparametric regression under covariate shift, where we observe samples from both the target distribution and a related but distinct source distribution. We introduce a novel object, the transfer function, and show that properties of its domain determine our minimax rates. Those exhibit a variety of regimes, including classical rates, governed by the better of source-only and target-only rates, as well as regimes in which the convergence rates exhibit multiplicative interactions between the sample sizes and are faster than the best-of-two benchmark. The rates are shown to be achieved up to logarithmic factors by a design-adaptive estimator. Compared with existing theory, our results cover the case in which covariates have unbounded support.
Keywords
Cite
@article{arxiv.2603.05897,
title = {A Minimax Theory of Nonparametric Regression Under Covariate Shift},
author = {Petr Zamolodtchikov},
journal= {arXiv preprint arXiv:2603.05897},
year = {2026}
}