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

• 成果类型: Article
• 署名作者: Mitra, Aritra; Richards, John A.; Sundaram, Shreyas
• 署名单位: Purdue University System; Purdue University; United States Department of Energy (DOE); Sandia National Laboratories
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3033126
• 发表日期: 2021
• 页码: 4084-4100
• 关键词: Laboratories; silicon; Analytical models; Bayes methods; entropy; STANDARDS; fault-tolerant control; inference algorithms; Multi-agent systems; Statistical learning

摘要

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), which 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.