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In this paper, we investigate the problem of robust ReconfigurableIntelligent Surface (RIS) phase-shifts configuration over heterogeneouscommunication environments. The problem is formulated as a distributed learningproblem over different environments in a Federated Learning (FL) setting.Equivalently, this corresponds to a game played between multiple RISs, aslearning agents, in heterogeneous environments. Using Invariant RiskMinimization (IRM) and its FL equivalent, dubbed FL Games, we solve the RISconfiguration problem by learning invariant causal representations acrossmultiple environments and then predicting the phases. The solution correspondsto playing according to Best Response Dynamics (BRD) which yields the NashEquilibrium of the FL game. The representation learner and the phase predictorare modeled by two neural networks, and their performance is validated viasimulations against other benchmarks from the literature. Our results show thatcausality-based learning yields a predictor that is 15% more accurate in unseenOut-of-Distribution (OoD) environments.

Federated Learning Games for Reconfigurable Intelligent Surfaces via Causal Representations