The Sample Complexity of Replicable Realizable PAC Learning
Machine Learning
2026-02-24 v1 Computational Complexity
Data Structures and Algorithms
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 dependence on the size of the hypothesis class . Our proof uses several novel techniques and works by defining a particular Cayley graph associated with 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.
Cite
@article{arxiv.2602.19552,
title = {The Sample Complexity of Replicable Realizable PAC Learning},
author = {Kasper Green Larsen and Markus Engelund Mathiasen and Chirag Pabbaraju and Clement Svendsen},
journal= {arXiv preprint arXiv:2602.19552},
year = {2026}
}