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arXiv · 2504.14572

Data Selection for ERMs

Steve Hanneke·Shay Moran·Alexander Shlimovich·Amir Yehudayoff
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Abstract

Learning theory has traditionally followed a model-centric approach, focusing on designing optimal algorithms for a fixed natural learning task (e.g., linear classification or regression). In this paper, we adopt a complementary data-centric perspective, whereby we fix a natural learning rule and focus on optimizing the training data. Specifically, we study the following question: given a learning rule $\mathcal{A}$ and a data selection budget $n$, how well can $\mathcal{A}$ perform when trained on at most $n$ data points selected from a population of $N$ points? We investigate when it is possible to select $n \ll N$ points and achieve performance comparable to training on the entire population. We address this question across a variety of empirical risk minimizers. Our results include optimal data-selection bounds for mean estimation, linear classification, and linear regression. Additionally, we establish two general results: a taxonomy of error rates in binary classification and in stochastic convex optimization. Finally, we propose several open questions and directions for future research.

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Steve Hanneke, Shay Moran, Alexander Shlimovich, Amir Yehudayoff. 2025-04-20. Data Selection for ERMs. https://arxiv.org/abs/2504.14572

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