A Communication-efficient Algorithm with Linear Convergence for Federated Minimax Learning
This work addresses communication inefficiency in federated learning for applications like GANs, offering a practical improvement over prior algorithms that either required frequent communication or had slow convergence rates.
The paper tackles the problem of slow convergence in federated minimax optimization by proposing FedGDA-GT, a gradient tracking-based algorithm that achieves linear convergence with constant stepsizes, requiring only O(log(1/ε)) communication rounds to reach an ε-approximation solution, and numerically outperforms existing methods like Local SGDA.
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-strongly-concave, we prove that FedGDA-GT converges linearly with a constant stepsize to global $ε$-approximation solution with $\mathcal{O}(\log (1/ε))$ rounds of communication, which matches the time complexity of centralized GDA method. Finally, we numerically show that FedGDA-GT outperforms Local SGDA.