The Optimal Sample Complexity of PAC Learning

TL;DR

This paper proves a tight upper bound on the number of samples needed for PAC learning in the realizable case, matching lower bounds and solving a longstanding open problem.

Contribution

It introduces a new upper bound on PAC sample complexity that aligns with known lower bounds, advancing theoretical understanding.

Findings

Established a tight upper bound on sample complexity for PAC learning

Matched the upper bound with known lower bounds up to constants

Solved a long-standing open problem in PAC learning theory

Abstract

This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the sample complexity of PAC learning. The technique and analysis build on a recent breakthrough by Hans Simon.