# A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction

arXiv: https://arxiv.org/abs/2204.00406 · HTML: https://mlsanity.com/paper/2204.00406/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 67 references that are in the map.
- First posted on arXiv 1 Apr 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)
- [Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivity](https://mlsanity.com/paper/1810.05633/) (2018)
- [Error bounds, quadratic growth, and linear convergence of proximal methods](https://mlsanity.com/paper/1602.06661/) (2016)
- [The importance of better models in stochastic optimization](https://mlsanity.com/paper/1903.08619/) (2019)
- [SEGA: Variance Reduction via Gradient Sketching](https://mlsanity.com/paper/1809.03054/) (2018)
- [SDPNAL+: A Majorized Semismooth Newton-CG Augmented Lagrangian Method for Semidefinite Programming with Nonnegative Constraints](https://mlsanity.com/paper/1406.0942/) (2014)
- [A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problems](https://mlsanity.com/paper/1607.05428/) (2016)
- [An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems](https://mlsanity.com/paper/1712.05910/) (2017)
- [A Stochastic Extra-Step Quasi-Newton Method for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1910.09373/) (2019)
- [A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1803.03466/) (2018)

## Built on by (most cited first, 5 of 5)

- [A Unified Convergence Theorem for Stochastic Optimization Methods](https://mlsanity.com/paper/2206.03907/) (2022)
- [Variance reduction techniques for stochastic proximal point algorithms](https://mlsanity.com/paper/2308.09310/) (2023)
- [Tracking the Median of Gradients with a Stochastic Proximal Point Method](https://mlsanity.com/paper/2402.12828/) (2024)
- [Step-Size Stability in Stochastic Optimization: A Theoretical Perspective](https://mlsanity.com/paper/2602.09842/) (2026)
- [Dual Certified White-Box Inference for Input Convex Neural Networks](https://mlsanity.com/paper/2605.04722/) (2026)

## Abstract (arXiv)

We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting SPP updates are solved using an inexact semismooth Newton framework. We establish detailed convergence results that take the inexactness of the SPP steps into account and that are in accordance with existing convergence guarantees of (proximal) stochastic variance-reduced gradient methods. Numerical experiments show that the proposed algorithm competes favorably with other state-of-the-art methods and achieves higher robustness with respect to the step size selection.