Mini-Batch Stochastic Three-Operator Splitting for Distributed Optimization

We consider a network of agents, each with its own private cost consisting sum two possibly nonsmooth convex functions, one which is composed linear operator. At every iteration agent performs local calculations and can only communicate neighbors. The challenging aspect our study that the smooth part function given as an expected value agents have access to this problem formulation via heavy-tailed stochastic oracle. To tackle such sampling-based optimization problems, we propose extension triangular pre-conditioned primal-dual algorithm. demonstrate almost sure convergence scheme validate performance method numerical experiments.