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Distributed Personalized Gradient Tracking with Convex Parametric Models

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Document pages: 27 pages

Abstract: We present a distributed optimization algorithm for solving onlinepersonalized optimization problems over a network of computing andcommunicating nodes, each of which linked to a specific user. The localobjective functions are assumed to have a composite structure and to consist ofa known time-varying (engineering) part and an unknown (user-specific) part.Regarding the unknown part, it is assumed to have a known parametric (e.g.,quadratic) structure a priori, whose parameters are to be learned along withthe evolution of the algorithm. The algorithm is composed of two intertwinedcomponents: (i) a dynamic gradient tracking scheme for finding local solutionestimates and (ii) a recursive least squares scheme for estimating the unknownparameters via user s noisy feedback on the local solution estimates. Thealgorithm is shown to exhibit a bounded regret under suitable assumptions.Finally, a numerical example corroborates the theoretical analysis.

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