# Stochastic DCA for minimizing a large sum of DC functions with application to Multi-class Logistic Regression

arXiv: https://arxiv.org/abs/1911.03992 · HTML: https://mlsanity.com/paper/1911.03992/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2019.

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

- [Sum of Ranked Range Loss for Supervised Learning](https://mlsanity.com/paper/2106.03300/) (2021)
- [Single-Loop Stochastic Algorithms for Difference of Max-Structured Weakly Convex Functions](https://mlsanity.com/paper/2405.18577/) (2024)

## Abstract (arXiv)

We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed: stochastic DCA and inexact stochastic DCA. We prove that the convergence of both algorithms to a critical point is guaranteed with probability one. Furthermore, we develop our stochastic DCA for solving an important problem in multi-task learning, namely group variables selection in multi class logistic regression. The corresponding stochastic DCA is very inexpensive, all computations are explicit. Numerical experiments on several benchmark datasets and synthetic datasets illustrate the efficiency of our algorithms and their superiority over existing methods, with respect to classification accuracy, sparsity of solution as well as running time.