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

arXiv: https://arxiv.org/abs/1907.03588 · HTML: https://mlsanity.com/paper/1907.03588/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Exploiting Heterogeneity in Robust Federated Best-Arm Identification](https://mlsanity.com/paper/2109.05700/) (2021)
- [Robust Online and Distributed Mean Estimation Under Adversarial Data Corruption](https://mlsanity.com/paper/2209.09624/) (2022)
- [Submodular Information Selection for Hypothesis Testing with Misclassification Penalties](https://mlsanity.com/paper/2405.10930/) (2024)
- [Classification with a Network of Partially Informative Agents: Enabling Wise Crowds from Individually Myopic Classifiers](https://mlsanity.com/paper/2409.19947/) (2024)
- [Robust Information Selection for Hypothesis Testing with Misclassification Penalties](https://mlsanity.com/paper/2502.14738/) (2025)

## Abstract (arXiv)

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.