# Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updates

arXiv: https://arxiv.org/abs/2306.05100 · HTML: https://mlsanity.com/paper/2306.05100/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 96 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Builds on (most cited first, 30 of 60)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Stochastic Gradient Push for Distributed Deep Learning](https://mlsanity.com/paper/1811.10792/) (2018)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach](https://mlsanity.com/paper/1901.08511/) (2019)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization](https://mlsanity.com/paper/2011.00364/) (2020)
- [A Unified Theory of SGD: Variance Reduction, Sampling, Quantization and Coordinate Descent](https://mlsanity.com/paper/1905.11261/) (2019)
- [The Complexity of Constrained Min-Max Optimization](https://mlsanity.com/paper/2009.09623/) (2020)
- [An Improved Analysis of Gradient Tracking for Decentralized Machine Learning](https://mlsanity.com/paper/2202.03836/) (2022)
- [A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games](https://mlsanity.com/paper/2206.05825/) (2022)
- [Negative Momentum for Improved Game Dynamics](https://mlsanity.com/paper/1807.04740/) (2018)
- [FedNest: Federated Bilevel, Minimax, and Compositional Optimization](https://mlsanity.com/paper/2205.02215/) (2022)
- [Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling](https://mlsanity.com/paper/2003.10162/) (2020)
- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [Stochastic Variance Reduction for Variational Inequality Methods](https://mlsanity.com/paper/2102.08352/) (2021)
- [The Complexity of Nonconvex-Strongly-Concave Minimax Optimization](https://mlsanity.com/paper/2103.15888/) (2021)
- [Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity](https://mlsanity.com/paper/2107.00052/) (2021)

## Built on by (most cited first, 4 of 4)

- [Multiplayer Federated Learning: Reaching Equilibrium with Less Communication](https://mlsanity.com/paper/2501.08263/) (2025)
- [Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularization](https://mlsanity.com/paper/2608.12043/) (2026)
- [Extragradient Method for (L0, L1)-Lipschitz Root-finding Problems](https://mlsanity.com/paper/2510.22421/) (2025)
- [Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes](https://mlsanity.com/paper/2406.02939/) (2024)

## Abstract (arXiv)

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.