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This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation type algorithm, namely the stochastic approximation proximal method of multipliers (PMMSopt) to solve this convex stochastic optimization problem. We analyze regrets of a stochastic approximation proximal method of multipliers for solving convex stochastic optimization problems. Under mild conditions, we show that this algorithm exhibits ${rm O}(T^{-1/2})$ rate of convergence, in terms of both optimality gap and constraint violation if parameters in the algorithm are properly chosen, when the objective and constraint functions are generally convex, where $T$ denotes the number of iterations. Moreover, we show that, with at least $1-e^{-T^{1/4}}$ probability, the algorithm has no more than ${rm O}(T^{-1/4})$ objective regret and no more than ${rm O}(T^{-1/8})$ constraint violation regret. To the best of our knowledge, this is the first time that such a proximal method for solving expectation constrained stochastic optimization is presented in the literature.
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal method of
We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to advances in
Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and nonconvex cases
Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic optimization proble
This paper considers a class of constrained convex stochastic composite optimization problems whose objective function is given by the summation of a differentiable convex component, together with a nonsmooth but convex component. The nonsmooth compo