Wednesday, December 9, 2020 - 4:00pm to 4:30pm
Event Calendar Category
LIDS & Stats Tea
Zoom meeting id
966 5151 6867
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We formulate gradient-based Markov chain Monte Carlo sampling as an optimization on the space of probability measures, with Kullback-Leibler divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.
Xiang is a postdoc in LIDS, hosted by Suvrit Sra. He is interested in the analysis of stochastic processes and their applications in machine learning. Xiang received his PhD in Computer Science from UC Berkeley, advised by Peter Bartlett and Michael I. Jordan.