# SAGDA: Achieving O(ε-2) Communication Complexity in Federated Min-Max Learning

arXiv: https://arxiv.org/abs/2210.00611 · HTML: https://mlsanity.com/paper/2210.00611/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 49 references that are in the map.
- First posted on arXiv 2 Oct 2022.

## Builds on (most cited first, 30 of 32)

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Communication-Efficient On-Device Machine Learning: Federated Distillation and Augmentation under Non-IID Private Data](https://mlsanity.com/paper/1811.11479/) (2018)
- [Don't Use Large Mini-Batches, Use Local SGD](https://mlsanity.com/paper/1808.07217/) (2018)
- [Achieving Linear Speedup with Partial Worker Participation in Non-IID Federated Learning](https://mlsanity.com/paper/2101.11203/) (2021)
- [SCAFFOLD: Stochastic Controlled Averaging for Federated Learning](https://mlsanity.com/paper/1910.06378/) (2019)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [SlowMo: Improving Communication-Efficient Distributed SGD with Slow Momentum](https://mlsanity.com/paper/1910.00643/) (2019)
- [Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms](https://mlsanity.com/paper/1808.07576/) (2018)
- [Robust Federated Learning: The Case of Affine Distribution Shifts](https://mlsanity.com/paper/2006.08907/) (2020)
- [On the convergence properties of a K-step averaging stochastic gradient descent algorithm for nonconvex optimization](https://mlsanity.com/paper/1708.01012/) (2017)
- [FedGAN: Federated Generative Adversarial Networks for Distributed Data](https://mlsanity.com/paper/2006.07228/) (2020)
- [Generative Models for Effective ML on Private, Decentralized Datasets](https://mlsanity.com/paper/1911.06679/) (2019)
- [Weakly-Convex Concave Min-Max Optimization: Provable Algorithms and Applications in Machine Learning](https://mlsanity.com/paper/1810.02060/) (2018)
- [Stochastic AUC Maximization with Deep Neural Networks](https://mlsanity.com/paper/1908.10831/) (2019)
- [STEM: A Stochastic Two-Sided Momentum Algorithm Achieving Near-Optimal Sample and Communication Complexities for Federated Learning](https://mlsanity.com/paper/2106.10435/) (2021)
- [Anarchic Federated Learning](https://mlsanity.com/paper/2108.09875/) (2021)
- [Local Stochastic Gradient Descent Ascent: Convergence Analysis and Communication Efficiency](https://mlsanity.com/paper/2102.13152/) (2021)
- [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms](https://mlsanity.com/paper/2203.04850/) (2022)
- [Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks](https://mlsanity.com/paper/2005.02426/) (2020)

## Abstract (arXiv)

To lower the communication complexity of federated min-max learning, a natural approach is to utilize the idea of infrequent communications (through multiple local updates) same as in conventional federated learning. However, due to the more complicated inter-outer problem structure in federated min-max learning, theoretical understandings of communication complexity for federated min-max learning with infrequent communications remain very limited in the literature. This is particularly true for settings with non-i.i.d. datasets and partial client participation. To address this challenge, in this paper, we propose a new algorithmic framework called stochastic sampling averaging gradient descent ascent (SAGDA), which i) assembles stochastic gradient estimators from randomly sampled clients as control variates and ii) leverages two learning rates on both server and client sides. We show that SAGDA achieves a linear speedup in terms of both the number of clients and local update steps, which yields an O(ε-2) communication complexity that is orders of magnitude lower than the state of the art. Interestingly, by noting that the standard federated stochastic gradient descent ascent (FSGDA) is in fact a control-variate-free special version of SAGDA, we immediately arrive at an O(ε-2) communication complexity result for FSGDA. Therefore, through the lens of SAGDA, we also advance the current understanding on communication complexity of the standard FSGDA method for federated min-max learning.