Federated Learning Games for Reconfigurable Intelligent Surfaces via Causal Representations

In this paper, we investigate the problem of robust Reconfigurable Intelligent Surface (RIS) phase-shifts configuration over heterogeneous communication environments. The problem is formulated as a distributed learning problem over different environments in a Federated Learning (FL) setting. Equivalently, this corresponds to a game played between multiple RISs, as learning agents, in heterogeneous environments. Using Invariant Risk Minimization (IRM) and its FL equivalent, dubbed FL Games, we solve the RIS configuration problem by learning invariant causal representations across multiple environments and then predicting the phases. The solution corresponds to playing according to Best Response Dynamics (BRD) which yields the Nash Equilibrium of the FL game. The representation learner and the phase predictor are modeled by two neural networks, and their performance is validated via simulations against other benchmarks from the literature. Our results show that causality-based learning yields a predictor that is 15% more accurate in unseen Out-of-Distribution (OoD) environments.