# Stochastic Three-Composite Convex Minimization

arXiv: https://arxiv.org/abs/1701.09033 · HTML: https://mlsanity.com/paper/1701.09033/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2017.

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

- [Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers](https://mlsanity.com/paper/2106.13067/) (2021)
- [humancompatible.train: Implementing Optimization Algorithms for Stochastically-Constrained Stochastic Optimization Problems](https://mlsanity.com/paper/2509.21254/) (2025)
- [Quadratic Objective Perturbation: Curvature-Based Differential Privacy](https://mlsanity.com/paper/2605.05905/) (2026)

## Abstract (arXiv)

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computationally advantageous to process smooth term in the decomposition with its stochastic gradient estimate and the other two functions separately with their proximal operators, such as doubly regularized empirical risk minimization problems. We prove the convergence characterization of the proposed algorithm in expectation under the standard assumptions for the stochastic gradient estimate of the smooth term. Our method operates in the primal space and can be considered as a stochastic extension of the three-operator splitting method. Numerical evidence supports the effectiveness of our method in real-world problems.