# Stochastic Approximation for Expectation Objective and Expectation Inequality-Constrained Nonconvex Optimization

arXiv: https://arxiv.org/abs/2307.02943 · HTML: https://mlsanity.com/paper/2307.02943/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2023.

## Built on by (most cited first, 3 of 3)

- [humancompatible.train: Implementing Optimization Algorithms for Stochastically-Constrained Stochastic Optimization Problems](https://mlsanity.com/paper/2509.21254/) (2025)
- [Benchmarking Stochastic Approximation Algorithms for Fairness-Constrained Training of Deep Neural Networks](https://mlsanity.com/paper/2507.04033/) (2025)
- [Stochastic Penalty-Barrier Method for Constrained Machine Learning](https://mlsanity.com/paper/2605.18618/) (2026)

## Abstract (arXiv)

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.