Distributed Energy-Aware Diffusion Least Mean Squares: Game-Theoretic Learning

TLDR: The convergence analysis shows that the parameter estimates weakly converge to the true parameter across the network, yet the global activation behavior along the way tracks the set of correlated equilibria of the underlying activation control game.

Abstract: This paper presents a game-theoretic approach to node activation control in parameter estimation via diffusion least mean squares (LMS). Nodes cooperate by exchanging estimates over links characterized by the connectivity graph of the network. The energy-aware activation control is formulated as a noncooperative repeated game where nodes autonomously decide when to activate based on a utility function that captures the trade-off between individual node's contribution and energy expenditure. The diffusion LMS stochastic approximation is combined with a game-theoretic learning algorithm such that the overall energy-aware diffusion LMS has two timescales: the fast timescale corresponds to the game-theoretic activation mechanism, whereby nodes distributively learn their optimal activation strategies, whereas the slow timescale corresponds to the diffusion LMS. The convergence analysis shows that the parameter estimates weakly converge to the true parameter across the network, yet the global activation behavior along the way tracks the set of correlated equilibria of the underlying activation control game.