Adaptive distributed methods under communication constraints

TL;DR

This paper investigates how to perform distributed estimation efficiently under communication limits in a nonparametric regression setting, establishing theoretical bounds and demonstrating adaptive methods that achieve optimal performance.

Contribution

It introduces adaptive estimation techniques for distributed nonparametric regression under communication constraints, achieving minimax optimality.

Findings

Derived minimax lower bounds for the problem

Developed methods that attain these bounds

Showed adaptive estimation is feasible in this context

Abstract

We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.