Federated Minimax Optimization: Improved Convergence Analyses and Algorithms

Pranay Sharma, Rohan Panda, Gauri Joshi, Pramod K. Varshney

Research output: Contribution to journalConference Articlepeer-review

15 Scopus citations

Abstract

In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications, such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has order-optimal sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys linear speedup with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments.

Original languageEnglish (US)
Pages (from-to)19683-19730
Number of pages48
JournalProceedings of Machine Learning Research
Volume162
StatePublished - 2022
Externally publishedYes
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: Jul 17 2022Jul 23 2022

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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