Title: Analysis of Langevin Monte Carlo via convex optimization
Authors: Blazej Miasojedow - University of Warsaw (Poland) [presenting]
Alain Durmus - CMLA - Ecole normale superieure Paris-Saclay (France)
Szymon Majewski - IMPAN (Poland)
Abstract: New insights are provided on the unadjusted Langevin algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order 2. Using this interpretation and techniques borrowed from convex optimization, we give a non-asymptotic analysis of this method to sample from logconcave smooth target distribution. Our proofs are then easily extended to the stochastic gradient Langevin dynamics, which is a popular extension of the unadjusted Langevin algorithm. Finally, this interpretation leads to a new methodology to sample from a non-smooth target distribution, for which a similar study is done.