Abstract: We consider a scenario where a group of agents, each receiving partially informative private signals, aim to learn the true underlying state of the world that explains their collective observations. These agents might represent individuals in a social network interacting to solve a day-to-day decision making problem, or a team of autonomous robots deployed with the task of environmental monitoring, or even a network of processors trying to solve a classification problem. To enable such agents to identify the true state from a finite set of hypotheses, 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 true state 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 strictly improves upon existing rates. We then consider a scenario where certain agents do not behave as expected, and deliberately try to spread misinformation. Capturing such misbehavior via the Byzantine adversary model, we develop a computationally-efficient variant of our learning rule that provably allows every regular agent to learn the true state exponentially fast, with probability 1.

Speaker Bio: Aritra Mitra received the B.E. degree from Jadavpur University, Kolkata, India, and the M.Tech. degree from the Indian Institute of Technology Kanpur, India, in 2013 and 2015, respectively, both in electrical engineering. He is currently working toward the Ph.D. degree in electrical engineering at the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA. His current research interests include the design of distributed algorithms for estimation, inference and learning; networked control systems; and secure control.  He was a recipient of the University Gold Medal at Jadavpur University, and the Academic Excellence Award at IIT Kanpur.