A Distributed Algorithm for Wasserstein Proximal Operator Splitting: Theory & Applications

Friday, November 4, 2022 14:00to15:00
Speaker: Abhishek Halder, Assistant Professor, Department of Applied Mathematics, University of California at Santa Cruz


Many problems in control, statistics, machine learning and solving partial differential equations can be cast as infinite dimensional gradient flows with respect to the Wasserstein metric that appears in the theory of optimal mass transport. The main idea is to construct the solution of interest as the gradient descent of a suitable measure valued functional that is convex along the generalized geodesics with respect to the Wasserstein metric. These connections have unfolded a rapid development across several disciplines in the past two decades. Many time stepping algorithms are now available in the literature to numerically realize the Wasserstein proximal updates, which generalize the concept of gradient steps in the manifold of probability measures with finite second moments. Motivated by the observation that most practical problems of interest have additive objectives, this talk will present a distributed algorithm to perform the Wasserstein proximal updates. The proposed algorithm generalizes the finite dimensional Euclidean consensus ADMM algorithm to the measure valued Wasserstein, and its entropy regularized Sinkhorn variants. We will point out how the proposed algorithm differs compared to the standard Euclidean case, and present numerical case studies. This is joint work with Ph.D. student Iman Nodozi at UC Santa Cruz.
Abhishek Halder is an Assistant Professor in the Department of Applied Mathematics, and an affiliated faculty in the Department of Electrical and Computer Engineering at University of California, Santa Cruz Before that he held postdoctoral positions in the Department of Mechanical and Aerospace Engineering at University of California, Irvine, and in the Department of Electrical and Computer Engineering at Texas A&M University He obtained his Bachelors and Masters from Indian Institute of Technology Kharagpur in 2008 and Ph D from Texas A&M University in 2014 all in Aerospace Engineering His research interests are in stochastic systems, control and optimization with application focus on large scale cyber physical systems He is a co-founder of the annual NorCal Control Workshop that brings together systems control researchers from academia and industry in the Northern California region fostering collaboration and professional networking.
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