# A New Approach to Distributed Hypothesis Testing and Non-Bayesian Learning: Improved Learning Rate and Byzantine-Resilience

## TL;DR

This paper introduces a novel distributed learning method for agents to identify the true state of the world, achieving faster convergence and resilience against malicious misinformation without belief-averaging.

## Contribution

It proposes a new belief update rule that outperforms existing methods in learning speed and robustness, including Byzantine resilience.

## Key findings

- Agents learn the true state almost surely
- False hypotheses are eliminated exponentially fast
- The method is resilient to Byzantine adversaries

## Abstract

We study a setting where a group of agents, each receiving partially informative private signals, seek to collaboratively learn the true underlying state of the world (from a finite set of hypotheses) that generates their joint observation profiles. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in that it does not employ any form of "belief-averaging". Instead, agents update their beliefs based on a min-rule. Under standard assumptions on the observation model and the network structure, we establish that each agent learns the truth asymptotically almost surely. As our main contribution, we prove that with probability 1, each false hypothesis is ruled out by every agent exponentially fast at a network-independent rate that is strictly larger than existing rates. We then develop a computationally-efficient variant of our learning rule that is provably resilient to agents who do not behave as expected (as represented by a Byzantine adversary model) and deliberately try to spread misinformation.