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Decentralized Hypothesis Testing on Graphs

Start Date: February 16, 2016 11:00 AM
End Date: February 16, 2016 12:00 PM

​Professor Angelia Nedich

University of Illinois

Abstract: We will consider the problem of distributed cooperative learning in a network of agents, where the agents are repeatedly gaining partial information about an unknown random variable whose distribution is to be jointly estimated. The learning is based on Bayesian update adapted to distributed information structure inherited from the network. The joint objective of the agent system is to globally agree on a hypothesis (distribution) that best describes the observed data by all agents in the network. Interactions between agents occur according to an unknown sequence of time-varying graphs. We highlight some interesting aspects of Bayesian learning and stochastic approximation approach for the case of a single agent, which has not been observed before and it allows for a new connection between optimization and statistical learning. Then, we discuss and analyze the general case where subsets of agents have conflicting hypothesis models, in the sense that the optimal solutions are different if the subset of agents were isolated. Additionally, we provide a new non-Bayesian learning protocol that converges an order of magnitude faster than the learning protocols currently available in the literature for arbitrary fixed undirected graphs. Our results establish consistency and a non-asymptotic, explicit, geometric convergence rate for the learning dynamics.

Bio: Angelia Nedich received her B.S. degree from the University of Montenegro (1987) and M.S. degree from the University of Belgrade (1990), both in Mathematics. She received her Ph.D. degrees from Moscow State University (1994) in Mathematics and Mathematical Physics, and from Massachusetts Institute of Technology in Electrical Engineering and Computer Science (2002). She has been at the BAE Systems Advanced Information Technology from 2002-2006. In Fall 2006, she has joined the Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign, USA.  She is a recipient of the NSF CAREER Award 2007 in Operations Research for her work in distributed multi-agent optimization. She has received the Donald Biggar Willett Scholar of Engineering Award (2013) and Dean’s Award for Excellence in Research (2015) from the College of Engineering at the University of Illinois at Urbana-Champaign.

Her general interest is in optimization and dynamics including fundamental theory, models, algorithms, and applications. Her current research interest is focused on large-scale convex optimization, distributed multi-agent optimization and equilibrium problems, stochastic approximations, and network aggregation-dynamics with applications in signal processing, machine learning, and decentralized control.