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arXiv · 2602.19552

The Sample Complexity of Replicable Realizable PAC Learning

Kasper Green Larsen·Markus Engelund Mathiasen·Chirag Pabbaraju·Clement Svendsen
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Abstract

In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the hypothesis class $H$. Our proof uses several novel techniques and works by defining a particular Cayley graph associated with $H$ and analyzing a suitable random walk on this graph by examining the spectral properties of its adjacency matrix. Furthermore, we show an almost matching upper bound for the lower bound instance, meaning if a stronger lower bound exists, one would have to consider a different instance of the problem.

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BibTeXRIS

Kasper Green Larsen, Markus Engelund Mathiasen, Chirag Pabbaraju, Clement Svendsen. 2026-02-23. The Sample Complexity of Replicable Realizable PAC Learning. https://arxiv.org/abs/2602.19552

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