论文标题
分散的Langevin动力学
Decentralized Langevin Dynamics
论文作者
论文摘要
Langevin MCMC梯度优化是估计后验分布的一类越来越流行的方法。本文介绍了在分散的设置中应用的算法，其中数据分布在一个代理网络中，这些网络使用点对点八卦通信来合作解决该问题。 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.
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.
