A Primal-Dual Algorithm for Distributed Stochastic Optimization with Equality Constraints

Distributed stochastic optimization problem with equality constraints over a random network with imperfect communications is considered, where the measurements of all functions to be used are subject to noises. The goal of the network is to minimize a global cost function subject to a global constraint set, where the global objective is a sum of objective functions, the global constraint set is the intersection of local constraint sets with equality constraints, and each agent only has access to information on its cost function and constraint function. A primal-dual projection-free distributed algorithm is proposed to solve the problem, where each agent updates its estimates by using the local observations and local information on its neighbors’ broadcast state values. Almost sure convergence of the algorithm is proven under mild conditions.