A Communication-efficient Algorithm with Linear Convergence for Federated Minimax Learning

Abstract

In this paper, we study a large-scale multi-agent minimax optimization problem, which models many interesting applications in statistical learning and game theory, including Generative Adversarial Networks (GANs). The overall objective is a sum of agents' private local objective functions. We first analyze an important special case, empirical minimax problem, where the overall objective approximates a true population minimax risk by statistical samples. We provide generalization bounds for learning with this objective through Rademacher complexity analysis. Then, we focus on the federated setting, where agents can perform local computation and communicate with a central server. Most existing federated minimax algorithms either require communication per iteration or lack performance guarantees with the exception of Local Stochastic Gradient Descent Ascent (SGDA), a multiple-local-update descent ascent algorithm which guarantees convergence under a diminishing stepsize. By analyzing Local SGDA under the ideal condition of no gradient noise, we show that generally it cannot guarantee exact convergence with constant stepsizes and thus suffers from slow rates of convergence. To tackle this issue, we propose FedGDA-GT, an improved Federated (Fed) Gradient Descent Ascent (GDA) method based on Gradient Tracking (GT). When local objectives are Lipschitz smooth and strongly-convex-stronglyconcave, we prove that FedGDA-GT converges linearly with a constant stepsize to global ǫ-approximation solution with O(log(1/ǫ)) rounds of communication, which matches the time complexity of centralized GDA method. Finally, we numerically show that FedGDA-GT outperforms Local SGDA.Preprint. Under review.

Particle-based Online Bayesian Sampling

“…The stochastic gradient descent algorithm is widely used as an incremental gradient algorithm that offers inexpensive iterations by approximating the gradient with a minibatch of observations. Through the past decade, it has been used in a wide variety of problems with different variations, like network optimization reinforcement learning (Liu et al, 2021b;a), federated learning (Sun and Wei, 2022) and recommendation system . However, this method, at the same time, incurs gradient error when approximating the gradient.…”

CDMA: A Practical Cross-Device Federated Learning Algorithm for General Minimax Problems

“…However, the computation of their global correction requires the full aggregation and thus do not apply to the cross-device setting. Besides, the analysis in (Sun and Wei 2022) focuses on strongly-convex-strongly-concave minimax problems, while we consider a class of nonconvexnonconcave problems, which are more challenging.…”

“…In this setting, the clients are numerous (up to 10 10 ( Kairouz et al 2019)) unreliable mobile/IoT devices with relatively slow network connections. Actually, most existing federated minimax algorithms are designed for another setting known as the cross-silo setting (Reisizadeh et al 2020;Rasouli, Sun, and Rajagopal 2020;Beznosikov, Samokhin, and Gasnikov 2020;Hou et al 2021;Guo et al 2020;Yuan et al 2021;Deng and Mahdavi 2021;Sharma et al 2022;Sun and Wei 2022), where the clients are a relatively small number of organizations or data centers with reliable network connections (Kairouz et al 2019). Compared with the cross-silo setting, it is generally more challenging to solve a problem in the cross-device setting due to the low client availability and relatively slow network connections (Kairouz et al 2019).…”