# Nonsmoothness in Machine Learning: specific structure, proximal identification, and applications

arXiv: https://arxiv.org/abs/2010.00848 · HTML: https://mlsanity.com/paper/2010.00848/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 9 of 9)

- [A Fast and Accurate Splitting Method for Optimal Transport: Analysis and Implementation](https://mlsanity.com/paper/2110.11738/) (2021)
- [Enhancing Privacy in Federated Learning through Local Training](https://mlsanity.com/paper/2403.17572/) (2024)
- [Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization](https://mlsanity.com/paper/2111.03820/) (2021)
- [Accelerating Frank-Wolfe via Averaging Step Directions](https://mlsanity.com/paper/2205.11794/) (2022)
- [Iterative regularization for low complexity regularizers](https://mlsanity.com/paper/2202.00420/) (2022)
- [Piecewise Polynomial Regression of Tame Functions via Integer Programming](https://mlsanity.com/paper/2311.13544/) (2023)
- [Faster Accelerated First-order Methods for Convex Optimization with Strongly Convex Function Constraints](https://mlsanity.com/paper/2212.11143/) (2022)
- [Reducing Discretization Error in the Frank-Wolfe Method](https://mlsanity.com/paper/2304.01432/) (2023)
- [Regularized Adaptive Momentum Dual Averaging with an Efficient Inexact Subproblem Solver for Training Structured Neural Network](https://mlsanity.com/paper/2403.14398/) (2024)

## Abstract (arXiv)

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine learning and illustrate how to leverage this structure in practice, for compression, acceleration, or dimension reduction. We pay a special attention to the presentation to make it concise and easily accessible, with both simple examples and general results.