We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a 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 with the evolution of the algorithm. The algorithm is composed of two intertwined components: (i) a dynamic gradient tracking scheme for finding local solution estimates and (ii) a recursive least squares scheme for estimating the unknown parameters via user's noisy feedback on the local solution estimates. The algorithm is shown to exhibit a bounded regret under suitable assumptions. Finally, a numerical example corroborates the theoretical analysis.

Notarnicola I., Simonetto A., Farina F., Notarstefano G. (2023). Distributed Personalized Gradient Tracking with Convex Parametric Models. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 68(1), 588-595 [10.1109/TAC.2022.3147007].

Distributed Personalized Gradient Tracking with Convex Parametric Models

Notarnicola I.
Primo
;
Simonetto A.
Secondo
;
Farina F.
Penultimo
;
Notarstefano G.
Ultimo
2023

Abstract

We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a 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 with the evolution of the algorithm. The algorithm is composed of two intertwined components: (i) a dynamic gradient tracking scheme for finding local solution estimates and (ii) a recursive least squares scheme for estimating the unknown parameters via user's noisy feedback on the local solution estimates. The algorithm is shown to exhibit a bounded regret under suitable assumptions. Finally, a numerical example corroborates the theoretical analysis.
2023
Notarnicola I., Simonetto A., Farina F., Notarstefano G. (2023). Distributed Personalized Gradient Tracking with Convex Parametric Models. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 68(1), 588-595 [10.1109/TAC.2022.3147007].
Notarnicola I.; Simonetto A.; Farina F.; Notarstefano G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/893058
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