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 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).

In the sequel, we empirically show the effect of different numbers of local updates on the fixed point. We consider cases withK = 1, K = 10, K = 20, K = 50. From Assumption 1, it is obvious thatgi(x,y) is convex-concave. Then, we conclude that there exists someη1 > 0 such that h(η) > 0, 0 < η < η1.

Byanalyzing 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.

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 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).

We focus on reducing communication overhead in multiplayer games, where frequently exchanging strategies between players is not feasible and players have noisy or outdated strategies of the other players. We introduce Decoupled SGDA, a novel adaptation of Stochastic Gradient Descent Ascent (SGDA). In this approach, players independently update their strategies based on outdated opponent strategies, with periodic synchronization to align strategies. For Strongly-Convex-Strongly-Concave (SCSC) games, we demonstrate that Decoupled SGDA achieves near-optimal communication complexity comparable to the best-known GDA rates. For weakly coupled games where the interaction between players is lower relative to the non-interactive part of the game, Decoupled SGDA significantly reduces communication costs compared to standard SGDA. Our findings extend to multi-player games. To provide insights into the effect of communication frequency and convergence, we extensively study the convergence of Decoupled SGDA for quadratic minimax problems. Lastly, in settings where the noise over the players is imbalanced, Decoupled SGDA significantly outperforms federated minimax methods.

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 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.

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 $\epsilon$-approximation solution with $\mathcal{O}(\log (1/\epsilon))$ rounds of communication, which matches the time complexity of centralized GDA method. Finally, we numerically show that FedGDA-GT outperforms Local SGDA.