Communication Bounds for the Distributed Experts Problem

TL;DR

This paper introduces communication-efficient protocols for the distributed experts problem, achieving near-optimal regret across various models and functions, with empirical validation showing significant savings.

Contribution

It presents the first near-optimal communication protocols for distributed experts problems under multiple models and functions, with theoretical bounds and empirical results.

Findings

Protocols achieve near-optimal regret with minimal communication

Conditional lower bounds show near-optimality of protocols

Empirical experiments demonstrate significant communication savings

Abstract

In this work, we study the experts problem in the distributed setting where an expert's cost needs to be aggregated across multiple servers. Our study considers various communication models such as the message-passing model and the broadcast model, along with multiple aggregation functions, such as summing and taking the $\ell_p$ norm of an expert's cost across servers. We propose the first communication-efficient protocols that achieve near-optimal regret in these settings, even against a strong adversary who can choose the inputs adaptively. Additionally, we give a conditional lower bound showing that the communication of our protocols is nearly optimal. Finally, we implement our protocols and demonstrate empirical savings on the HPO-B benchmarks.