Stochastic Gradient Langevin Dynamics on a Distributed Network

01/02/2020

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by   Vyacheslav Kungurtsev, et al.

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Langevin MCMC gradient optimization is a class of increasingly popular methods for estimating a posterior distribution. This paper addresses the algorithm as applied in a decentralized setting, wherein data is distributed across a network of agents which act to cooperatively solve the problem using peer-to-peer gossip communication. We show, theoretically, results in 1) the time-complexity to ϵ-consensus for the continuous time stochastic differential equation, 2) convergence rate in L^2 norm to consensus for the discrete implementation as defined by the Euler-Maruyama discretization and 3) convergence rate in the Wasserstein metric to the optimal stationary distribution for the discretized dynamics.