Best Response Dynamics Convergence for Generalized Nash Equilibrium Problems: An Opportunity for Autonomous Multiple Access Design in Federated Learning

Federated learning (FL) is envisioned to be a key enabler of network functionalities based on artificial intelligence. Multiple access mechanisms supporting the learning task must then be designed, in order to provide an efficient interplay between the communication and computation resources. This work considers thus a multilevel slotted random access scheme autonomously optimized by each node. Due to their mutual coupling, the nodes’ interaction is an instance of the best response dynamics (BRD) of a generalized Nash equilibrium problem (GNEP). Within this framework, levers are identified, guaranteeing the convergence of the interactions to an equilibrium point at which the FL task is supported. These levers, on which the network manager can act, are validated by numerical simulations. These latter moreover show that the performance loss due to the autonomous character of the nodes is negligible with respect to the result of a centralized optimization. On a broader mathematical level, this work defines a class of GNEPs for which sufficient convergence conditions for the totally asynchronous BRD are obtained. The considered class, named the GNEPs with polyhedral strategy sets and variable right-hand sides, encompasses a wide variety of GNEPs, and in particular GNEPs which are neither jointly convex nor generalized potential games. The obtained conditions depend on the first and second derivatives of the objective and constraint functions, and they constitute thus an off-the-shelf framework to study the BRD of GNEPs belonging to the identified class.