Tight Bounds for Collaborative PAC Learning via Multiplicative Weights

TL;DR

This paper presents a new collaborative PAC learning algorithm with improved overhead bounds, demonstrating near-optimal performance and superior empirical results on real datasets.

Contribution

It introduces an algorithm with $O( ext{log }k)$ overhead, improving previous bounds, and proves this bound is nearly optimal, supported by empirical validation.

Findings

Achieved $O( ext{log }k)$ overhead in collaborative PAC learning.

Proved $ ext{Omega}( ext{log }k)$ overhead is unavoidable.

Demonstrated superior empirical performance on real-world datasets.

Abstract

We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target function well on all players' distributions simultaneously. The quality of the collaborative learning algorithm is measured by the ratio between the sample complexity of the algorithm and that of the learning algorithm for a single distribution (called the overhead). We obtain a collaborative learning algorithm with overhead $O(\ln k)$, improving the one with overhead $O(\ln^2 k)$ in \cite{BHPQ17}. We also show that an $\Omega(\ln k)$ overhead is inevitable when $k$ is polynomial bounded by the VC dimension of the hypothesis class. Finally, our experimental study has demonstrated the superiority of our algorithm compared with the one in Blum et al. on real-world datasets.