Adaptive primal-dual stochastic gradient method for expectation-constrained convex stochastic programs

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 problems with expectation For these problems, it is often extremely expensive to perform projection onto the feasible set. Several SGMs in literature can be applied solve expectation-constrained We propose a novel primal-dual type SGM based on Lagrangian function. Different from methods, our method incorporates an adaptiveness technique speed up convergence. At each iteration, inquires unbiased subgradient function, and then renews primal variables by adaptive-SGM update dual vanilla-SGM update. show that proposed has convergence rate $$O(1/\sqrt{k})$$ terms objective error constraint violation. Although same as those SGMs, observe its significantly faster than non-adaptive Neyman–Pearson classification quadratically constrained quadratic programs. Furthermore, modify convex–concave minimax which updates both variables. also established modified gap. Our code released at https://github.com/RPI-OPT/APriD .