Jeffrey J. Ma

Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents’ actions. While gradient descent is a reliable basic workhorse for single-agent optimization, it often leads to oscillation in competitive optimization. In this work we propose polymatrix competitive gradient descent (PCGD) as a method for solving general sum competitive optimization involving arbitrary numbers of agents. The updates of our method are obtained as the Nash equilibria of a local polymatrix approximation with a quadratic regularization, and can be computed efficiently by solving a linear system of equations. We prove local convergence of PCGD to stable fixed points for n-player general-sum games, and show that it does not require adapting the step size to the strength of the player-interactions. We use PCGD to optimize policies in multi-agent reinforcement learning and demonstrate its advantages in Snake, Markov soccer and an electricity market game. Agents trained by PCGD outperform agents trained with simultaneous gradient descent, symplectic gradient adjustment, and extragradient in Snake and Markov soccer games and on the electricity market game, PCGD trains faster than both simultaneous gradient descent and the extragradient method.

Federated Learning (FL) endeavors to harness decentralized data while preserving privacy, facing challenges of performance, scalability, and collaboration. Asynchronous Federated Learning (AFL) methods have emerged as promising alternatives to their synchronous counterparts bounded by the slowest agent, yet they add additional challenges in convergence guarantees, fairness with respect to compute heterogeneity, and incorporation of staleness in aggregated updates. Specifically, AFL biases model training heavily towards agents who can produce updates faster, leaving slower agents behind, who often also have differently distributed data which is not learned by the global model. Naively upweighting introduces incentive issues, where true fast updating agents may falsely report updates at a slower speed to increase their contribution to model training. We introduce FedStaleWeight, an algorithm addressing fairness in aggregating asynchronous client updates by employing average staleness to compute fair re-weightings. FedStaleWeight reframes asynchronous federated learning aggregation as a mechanism design problem, devising a weighting strategy that incentivizes truthful compute speed reporting without favoring faster update-producing agents by upweighting agent updates based on staleness. Leveraging only observed agent update staleness, FedStaleWeight results in more equitable aggregation on a per-agent basis. We both provide theoretical convergence guarantees in the smooth, non-convex setting and empirically compare FedStaleWeight against the commonly used asynchronous FedBuff with gradient averaging, demonstrating how it achieves stronger fairness, expediting convergence to a higher global model accuracy. Finally, we provide an open-source test bench to facilitate exploration of buffered AFL aggregation strategies, fostering further research in asynchronous federated learning paradigms.