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Modified Frank Wolfe in Probability Space
Carson Kent · Jiajin Li · Jose Blanchet · Peter W Glynn

Tue Dec 07 04:30 PM -- 06:00 PM (PST) @

We propose a novel Frank-Wolfe (FW) procedure for the optimization of infinite-dimensional functionals of probability measures - a task which arises naturally in a wide range of areas including statistical learning (e.g. variational inference) and artificial intelligence (e.g. generative adversarial networks). Our FW procedure takes advantage of Wasserstein gradient flows and strong duality results recently developed in Distributionally Robust Optimization so that gradient steps (in the Wasserstein space) can be efficiently computed using finite-dimensional, convex optimization methods. We show how to choose the step sizes in order to guarantee exponentially fast iteration convergence, under mild assumptions on the functional to optimize. We apply our algorithm to a range of functionals arising from applications in nonparametric estimation.

Author Information

Carson Kent (Stanford University)
Jiajin Li (The Chinese University of Hong Kong)
Jose Blanchet (Stanford University)
Peter W Glynn (Stanford University)

Peter W. Glynn is the Thomas Ford Professor in the Department of Management Science and Engineering (MS&E) at Stanford University, and also holds a courtesy appointment in the Department of Electrical Engineering. He received his Ph.D in Operations Research from Stanford University in 1982. He then joined the faculty of the University of Wisconsin at Madison, where he held a joint appointment between the Industrial Engineering Department and Mathematics Research Center, and courtesy appointments in Computer Science and Mathematics. In 1987, he returned to Stanford, where he joined the Department of Operations Research. He was Director of Stanford's Institute for Computational and Mathematical Engineering from 2006 until 2010 and served as Chair of MS&E from 2011 through 2015. He is a Fellow of INFORMS and a Fellow of the Institute of Mathematical Statistics, and was an IMS Medallion Lecturer in 1995 and INFORMS Markov Lecturer in 2014. He was co-winner of the Outstanding Publication Awards from the INFORMS Simulation Society in 1993, 2008, and 2016, was a co-winner of the Best (Biannual) Publication Award from the INFORMS Applied Probability Society in 2009, and was the co-winner of the John von Neumann Theory Prize from INFORMS in 2010. In 2012, he was elected to the National Academy of Engineering. He was Founding Editor-in-Chief of Stochastic Systems and is currently Editor-in-Chief of Journal of Applied Probability and Advances in Applied Probability. His research interests lie in simulation, computational probability, queueing theory, statistical inference for stochastic processes, and stochastic modeling.

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