Smoothed First-order Algorithms for Expectation-valued Constrained Problems

We consider the development of first-order algorithms for convex stochastic optimization problems with expectation constraints. By recasting the problem as a solution to a monotone stochastic variational inequality problem, we note that a solution to this problem can be obtained as a solution to an unconstrained nonsmooth convex stochastic optimization problem. We utilize a variance-reduced smoothed first-order scheme for resolving such a problem and derive rate statements for such a scheme.