Communication-efficient Distributed Cooperative Learning with Compressed Beliefs

TL;DR

This paper introduces a communication-efficient distributed learning algorithm where agents share compressed beliefs, achieving exponential convergence and significantly reducing communication costs.

Contribution

The paper proposes a novel belief update rule with compressed communication that guarantees convergence and reduces communication overhead in distributed learning.

Findings

Beliefs converge exponentially to the optimal hypotheses set.

Communication cost is reduced to 5-10% of non-compressed methods.

The method is supported by numerical experiments demonstrating efficiency.

Abstract

We study the problem of distributed cooperative learning, where a group of agents seeks to agree on a set of hypotheses that best describes a sequence of private observations. In the scenario where the set of hypotheses is large, we propose a belief update rule where agents share compressed (either sparse or quantized) beliefs with an arbitrary positive compression rate. Our algorithm leverages a unified communication rule that enables agents to access wide-ranging compression operators as black-box modules. We prove the almost sure asymptotic exponential convergence of beliefs around the set of optimal hypotheses. Additionally, we show a non-asymptotic, explicit, and linear concentration rate in probability of the beliefs on the optimal hypothesis set. We provide numerical experiments to illustrate the communication benefits of our method. The simulation results show that the number of transmitted bits can be reduced to 5-10% of the non-compressed method in the studied scenarios.