# Switch and Conquer: Efficient Algorithms By Switching Stochastic Gradient Oracles For Decentralized Saddle Point Problems

arXiv: https://arxiv.org/abs/2309.00997 · HTML: https://mlsanity.com/paper/2309.00997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Builds on (most cited first, 20 of 20)

- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [Distributed Learning with Compressed Gradient Differences](https://mlsanity.com/paper/1901.09269/) (2019)
- [Stochastic Variance Reduction Methods for Saddle-Point Problems](https://mlsanity.com/paper/1605.06398/) (2016)
- [Communication-Efficient Algorithms for Decentralized and Stochastic Optimization](https://mlsanity.com/paper/1701.03961/) (2017)
- [A Decentralized Parallel Algorithm for Training Generative Adversarial Nets](https://mlsanity.com/paper/1910.12999/) (2019)
- [Multi-Agent Reinforcement Learning via Double Averaging Primal-Dual Optimization](https://mlsanity.com/paper/1806.00877/) (2018)
- [Linear Convergent Decentralized Optimization with Compression](https://mlsanity.com/paper/2007.00232/) (2020)
- [Stochastic Primal-Dual Algorithms with Faster Convergence than O(1/√T) for Problems without Bilinear Structure](https://mlsanity.com/paper/1904.10112/) (2019)
- [Stop Wasting My Gradients: Practical SVRG](https://mlsanity.com/paper/1511.01942/) (2015)
- [Optimal Algorithms for Decentralized Stochastic Variational Inequalities](https://mlsanity.com/paper/2202.02771/) (2022)
- [Decentralized Stochastic Gradient Descent Ascent for Finite-Sum Minimax Problems](https://mlsanity.com/paper/2212.02724/) (2022)
- [Decentralized Distributed Optimization for Saddle Point Problems](https://mlsanity.com/paper/2102.07758/) (2021)
- [Communication-Efficient Distributionally Robust Decentralized Learning](https://mlsanity.com/paper/2205.15614/) (2022)
- [Distributed Saddle-Point Problems Under Similarity](https://mlsanity.com/paper/2107.10706/) (2021)
- [Decentralized Composite Optimization with Compression](https://mlsanity.com/paper/2108.04448/) (2021)
- [Distributed saddle-point subgradient algorithms with Laplacian averaging](https://mlsanity.com/paper/1510.05169/) (2015)
- [Distributed saddle point problems for strongly concave-convex functions](https://mlsanity.com/paper/2202.05812/) (2022)
- [Stochastic Gradient Methods with Compressed Communication for Decentralized Saddle Point Problems](https://mlsanity.com/paper/2205.14452/) (2022)

## Abstract (arXiv)

We consider a class of non-smooth strongly convex-strongly concave saddle point problems in a decentralized setting without a central server. To solve a consensus formulation of problems in this class, we develop an inexact primal dual hybrid gradient (inexact PDHG) procedure that allows generic gradient computation oracles to update the primal and dual variables. We first investigate the performance of inexact PDHG with stochastic variance reduction gradient (SVRG) oracle. Our numerical study uncovers a significant phenomenon of initial conservative progress of iterates of IPDHG with SVRG oracle. To tackle this, we develop a simple and effective switching idea, where a generalized stochastic gradient (GSG) computation oracle is employed to hasten the iterates' progress to a saddle point solution during the initial phase of updates, followed by a switch to the SVRG oracle at an appropriate juncture. The proposed algorithm is named Decentralized Proximal Switching Stochastic Gradient method with Compression (C-DPSSG), and is proven to converge to an ε-accurate saddle point solution with linear rate. Apart from delivering highly accurate solutions, our study reveals that utilizing the best convergence phases of GSG and SVRG oracles makes C-DPSSG well suited for obtaining solutions of low/medium accuracy faster, useful for certain applications. Numerical experiments on two benchmark machine learning applications show C-DPSSG's competitive performance which validate our theoretical findings. The codes used in the experiments can be found hrefhttps://github.com/chhavisharma123/C-DPSSG-CDC2023here.