Stochastic Augmented Lagrangian Framework with Second-Order Convergence Guarantees for Nonconvex Expectation-Constrained Optimization

In this paper, we propose and analyze an augmented Lagrangian framework for solving stochastic nonconvex optimization problems with expectation-based equality constraints over a closed and convex constraint set. The framework generates a sequence of nonconvex primal subproblems, which are solved ine