# Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers

arXiv: https://arxiv.org/abs/2106.13067 · HTML: https://mlsanity.com/paper/2106.13067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 70 references that are in the map.
- First posted on arXiv 24 Jun 2021.

## Builds on (most cited first, 30 of 36)

- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile](https://mlsanity.com/paper/1807.02629/) (2018)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [On the convergence of single-call stochastic extra-gradient methods](https://mlsanity.com/paper/1908.08465/) (2019)
- [Achieving Fairness through Adversarial Learning: an Application to Recidivism Prediction](https://mlsanity.com/paper/1807.00199/) (2018)
- [Gradient descent GAN optimization is locally stable](https://mlsanity.com/paper/1706.04156/) (2017)
- [Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling](https://mlsanity.com/paper/2003.10162/) (2020)
- [A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity](https://mlsanity.com/paper/1808.04162/) (2018)
- [A Three-Operator Splitting Scheme and its Optimization Applications](https://mlsanity.com/paper/1504.01032/) (2015)
- [Context-Aware Generative Adversarial Privacy](https://mlsanity.com/paper/1710.09549/) (2017)
- [Improved Adversarial Learning for Fair Classification](https://mlsanity.com/paper/1901.10443/) (2019)
- [Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants](https://mlsanity.com/paper/1410.1628/) (2014)
- [Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization](https://mlsanity.com/paper/2104.13326/) (2021)
- [Taming GANs with Lookahead-Minmax](https://mlsanity.com/paper/2006.14567/) (2020)
- [Two steps at a time -- taking GAN training in stride with Tseng's method](https://mlsanity.com/paper/2006.09033/) (2020)
- [Adaptive Three Operator Splitting](https://mlsanity.com/paper/1804.02339/) (2018)
- [Rare Feature Selection in High Dimensions](https://mlsanity.com/paper/1803.06675/) (2018)
- [Forward-backward-forward methods with variance reduction for stochastic variational inequalities](https://mlsanity.com/paper/1902.03355/) (2019)
- [Asynchronous Block-Iterative Primal-Dual Decomposition Methods for Monotone Inclusions](https://mlsanity.com/paper/1507.03291/) (2015)
- [Stochastic Three-Composite Convex Minimization](https://mlsanity.com/paper/1701.09033/) (2017)
- [Generative Minimization Networks: Training GANs Without Competition](https://mlsanity.com/paper/2103.12685/) (2021)

## Built on by (most cited first, 1 of 1)

- [Variance Reduced Halpern Iteration for Finite-Sum Monotone Inclusions](https://mlsanity.com/paper/2310.02987/) (2023)

## Abstract (arXiv)

We present a new, stochastic variant of the projective splitting (PS) family of algorithms for monotone inclusion problems. It can solve min-max and noncooperative game formulations arising in applications such as robust ML without the convergence issues associated with gradient descent-ascent, the current de facto standard approach in such situations. Our proposal is the first version of PS able to use stochastic (as opposed to deterministic) gradient oracles. It is also the first stochastic method that can solve min-max games while easily handling multiple constraints and nonsmooth regularizers via projection and proximal operators. We close with numerical experiments on a distributionally robust sparse logistic regression problem.