Distributed Learning, Communication Complexity and Privacy

TL;DR

This paper investigates the communication complexity of PAC-learning from distributed data, providing bounds, algorithms, and privacy considerations, with applications to various concept classes and learning settings.

Contribution

It introduces new bounds and algorithms for distributed learning, incorporating concepts like teaching-dimension and mistake-bound, and explores privacy aspects in this context.

Findings

Tight bounds for common concept classes like conjunctions and parity functions.

Efficient distributed Perceptron algorithm for linear separators under certain distributions.

A generic boosting approach achieving logarithmic communication dependence on 1/epsilon.

Abstract

We consider the problem of PAC-learning from distributed data and analyze fundamental communication complexity questions involved. We provide general upper and lower bounds on the amount of communication needed to learn well, showing that in addition to VC-dimension and covering number, quantities such as the teaching-dimension and mistake-bound of a class play an important role. We also present tight results for a number of common concept classes including conjunctions, parity functions, and decision lists. For linear separators, we show that for non-concentrated distributions, we can use a version of the Perceptron algorithm to learn with much less communication than the number of updates given by the usual margin bound. We also show how boosting can be performed in a generic manner in the distributed setting to achieve communication with only logarithmic dependence on 1/epsilon for any concept class, and demonstrate how recent work on agnostic learning from class-conditional queries can be used to achieve low communication in agnostic settings as well. We additionally present an analysis of privacy, considering both differential privacy and a notion of distributional privacy that is especially appealing in this context.