Parallel Best Arm Identification in Heterogeneous Environments

TL;DR

This paper investigates the challenges of parallel best arm identification in heterogeneous environments, revealing that collaboration complexity increases compared to homogeneous settings, with tight bounds on time and communication tradeoffs.

Contribution

It provides the first tight bounds on the time and communication tradeoffs for best arm identification in heterogeneous collaborative learning environments.

Findings

Heterogeneous environments are more challenging than homogeneous ones.

Almost tight upper and lower bounds are established.

Collaboration complexity increases in heterogeneous settings.

Abstract

In this paper, we study the tradeoffs between the time and the number of communication rounds of the best arm identification problem in the heterogeneous collaborative learning model, where multiple agents interact with possibly different environments and they want to learn in parallel an objective function in the aggregated environment. By proving almost tight upper and lower bounds, we show that collaborative learning in the heterogeneous setting is inherently more difficult than that in the homogeneous setting in terms of the time-round tradeoff.