# Stochastic Proximal Methods for Non-Smooth Non-Convex Constrained Sparse Optimization

## TL;DR

This paper introduces stochastic proximal gradient methods for non-smooth, non-convex constrained optimization, providing the first non-asymptotic convergence analysis and demonstrating superior empirical performance over deterministic algorithms.

## Contribution

It presents the first non-asymptotic convergence results for stochastic proximal methods in non-smooth, non-convex constrained settings and introduces algorithms with improved convergence complexities.

## Key findings

- Algorithms outperform state-of-the-art deterministic methods in experiments.
- First non-asymptotic convergence results for this class of problems.
- Algorithms show superior convergence in numerical tests.

## Abstract

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic convergence results for this class of problem. We present two simple stochastic proximal gradient algorithms, for general stochastic and finite-sum optimization problems, which have the same or superior convergence complexities compared to the current best results for the unconstrained problem setting. In a numerical experiment we compare our algorithms with the current state-of-the-art deterministic algorithm and find our algorithms to exhibit superior convergence.

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Source: https://tomesphere.com/paper/1905.10188