# Stochastic Optimization for Non-convex Inf-Projection Problems

arXiv: https://arxiv.org/abs/1908.09941 · HTML: https://mlsanity.com/paper/1908.09941/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2019.

## Built on by (most cited first, 2 of 2)

- [Almost Linear Constant-Factor Sketching for ℓ1 and Logistic Regression](https://mlsanity.com/paper/2304.00051/) (2023)
- [Scalable Distributional Robustness in a Class of Non Convex Optimization with Guarantees](https://mlsanity.com/paper/2205.15624/) (2022)

## Abstract (arXiv)

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cases. We develop stochastic algorithms and establish their first-order convergence for finding a (nearly) stationary solution of the target non-convex function under different conditions of the component functions. To the best of our knowledge, this is the first work that comprehensively studies stochastic optimization of non-convex inf-projection minimization problems with provable convergence guarantee. Our algorithms enable efficient stochastic optimization of a family of non-decomposable DC functions and a family of bi-convex functions. To demonstrate the power of the proposed algorithms we consider an important application in variance-based regularization. Experiments verify the effectiveness of our inf-projection based formulation and the proposed stochastic algorithm in comparison with previous stochastic algorithms based on the min-max formulation for achieving the same effect.