Adaptive Federated Minimax Optimization with Lower Complexities

TL;DR

This paper introduces AdaFGDA, an adaptive federated minimax optimization algorithm that reduces gradient and communication complexities for nonconvex problems, with theoretical guarantees and practical effectiveness.

Contribution

The paper proposes AdaFGDA, a novel adaptive federated minimax algorithm with lower complexities and convergence guarantees under non-i.i.d. data settings.

Findings

Achieves lower gradient complexity of  O(psilon^{-3})

Reduces communication complexity to  O(psilon^{-2})

Demonstrates effectiveness on deep AUC maximization and robust neural network training

Abstract

Federated learning is a popular distributed and privacy-preserving learning paradigm in machine learning. Recently, some federated learning algorithms have been proposed to solve the distributed minimax problems. However, these federated minimax algorithms still suffer from high gradient or communication complexity. Meanwhile, few algorithm focuses on using adaptive learning rate to accelerate these algorithms. To fill this gap, in the paper, we study a class of nonconvex minimax optimization, and propose an efficient adaptive federated minimax optimization algorithm (i.e., AdaFGDA) to solve these distributed minimax problems. Specifically, our AdaFGDA builds on the momentum-based variance reduced and local-SGD techniques, and it can flexibly incorporate various adaptive learning rates by using the unified adaptive matrices. Theoretically, we provide a solid convergence analysis framework for our AdaFGDA algorithm under non-i.i.d. setting. Moreover, we prove our AdaFGDA algorithm obtains a lower gradient (i.e., stochastic first-order oracle, SFO) complexity of $\tilde{O}(\epsilon^{-3})$ with lower communication complexity of $\tilde{O}(\epsilon^{-2})$ in finding $\epsilon$-stationary point of the nonconvex minimax problems. Experimentally, we conduct some experiments on the deep AUC maximization and robust neural network training tasks to verify efficiency of our algorithms.