Nonasymptotic Convergence Rates for Cooperative Learning Over Time-Varying Directed Graphs

TL;DR

This paper establishes explicit, non-asymptotic convergence rates for distributed hypothesis testing over time-varying directed networks, demonstrating how agents collaboratively learn the best hypothesis efficiently.

Contribution

It introduces a non-asymptotic analysis of a Bayesian-based distributed learning algorithm over dynamic directed graphs, providing explicit convergence rates.

Findings

Agents reach consensus on the best hypothesis under strong connectivity.

The convergence rate is geometric and explicitly characterized.

The method extends to time-varying directed network topologies.

Abstract

We study the problem of distributed hypothesis testing with a network of agents where some agents repeatedly gain access to information about the correct hypothesis. The group objective is to globally agree on a joint hypothesis that best describes the observed data at all the nodes. We assume that the agents can interact with their neighbors in an unknown sequence of time-varying directed graphs. Following the pioneering work of Jadbabaie, Molavi, Sandroni, and Tahbaz-Salehi, we propose local learning dynamics which combine Bayesian updates at each node with a local aggregation rule of private agent signals. We show that these learning dynamics drive all agents to the set of hypotheses which best explain the data collected at all nodes as long as the sequence of interconnection graphs is uniformly strongly connected. Our main result establishes a non-asymptotic, explicit, geometric convergence rate for the learning dynamic.