Stochastic Approximation for Expectation Objective and Expectation Inequality-Constrained Nonconvex Optimization
Abstract
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a practitioner requires the system to adhere to, as well as the objective, which typically involves some empirical loss. We present the first stochastic approximation approach for solving this class of problems using the Ghost framework of incorporating penalty functions for analysis of a sequential convex programming approach together with a Monte Carlo estimator of nonlinear maps. We provide almost sure convergence guarantees and demonstrate the performance of the procedure on some representative examples.
Cite
@article{arxiv.2307.02943,
title = {Stochastic Approximation for Expectation Objective and Expectation Inequality-Constrained Nonconvex Optimization},
author = {Francisco Facchinei and Vyacheslav Kungurtsev},
journal= {arXiv preprint arXiv:2307.02943},
year = {2025}
}
Comments
DISCLAIMER: Unfortunately, this manuscript was originally associated as part of a Horizon project that was later uncovered to exhibit egregious ethical problems. The authors hereby declare that we DO NOT approve of any use of the algorithm therein for use in the activities of the project AutoFair led by Marecek, or related