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We propose a new algorithm---Stochastic Proximal Langevin Algorithm(SPLA)---for sampling from a log concave distribution. Our method is ageneralization of the Langevin algorithm to potentials expressed as the sum ofone stochastic smooth term and multiple stochastic nonsmooth terms. In eachiteration, our splitting technique only requires access to a stochasticgradient of the smooth term and a stochastic proximal operator for each of thenonsmooth terms. We establish nonasymptotic sublinear and linear convergencerates under convexity and strong convexity of the smooth term, respectively,expressed in terms of the KL divergence and Wasserstein distance. We illustratethe efficiency of our sampling technique through numerical simulations on aBayesian learning task.

Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates