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Optimal multiclass overfitting by sequence reconstruction from Hamming queries

Abstract

A primary concern of excessive reuse of test datasets in machine learning is that it can lead to overfitting. Multiclass classification was recently shown to be more resistant to overfitting than binary classification. In an open problem of COLT 2019, Feldman, Frostig, and Hardt ask to characterize the dependence of the amount of overfitting bias with the number of classes mm, the number of accuracy queries kk, and the number of examples in the dataset nn. We resolve this problem and determine the amount of overfitting possible in multi-class classification. We provide computationally efficient algorithms that achieve overfitting bias of Θ~(max{k/(mn),k/n})\tilde{\Theta}(\max\{\sqrt{{k}/{(mn)}}, k/n\}), matching the known upper bounds.

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