# A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

## TL;DR

This paper introduces a novel distributed hypothesis testing method where agents update beliefs without averaging, ensuring convergence to the true state even with Byzantine adversaries, under minimal assumptions.

## Contribution

The paper presents a belief update rule that avoids belief-averaging and extends to Byzantine-resilient scenarios, with proven asymptotic correctness.

## Key findings

- Agents' beliefs asymptotically concentrate on the true state.
- The method is resilient to Byzantine adversaries under certain conditions.
- Convergence is guaranteed with minimal assumptions on signals and network topology.

## Abstract

We study a setting where a group of agents, each receiving partially informative private observations, seek to collaboratively learn the true state (among a set of hypotheses) that explains their joint observation profiles over time. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in the sense, that it does not employ any form of "belief-averaging". Specifically, every agent maintains a local belief (on each hypothesis) that is updated in a Bayesian manner without any network influence, and an actual belief that is updated (up to normalization) as the minimum of its own local belief and the actual beliefs of its neighbors. Under minimal requirements on the signal structures of the agents and the underlying communication graph, we establish consistency of the proposed belief update rule, i.e., we show that the actual beliefs of the agents asymptotically concentrate on the true state almost surely. As one of the key benefits of our approach, we show that our learning rule can be extended to scenarios that capture misbehavior on the part of certain agents in the network, modeled via the Byzantine adversary model. In particular, we prove that each non-adversarial agent can asymptotically learn the true state of the world almost surely, under appropriate conditions on the observation model and the network topology.