Distributed Personalized Gradient Tracking With Convex Parametric Models

• 成果类型: Article
• 署名作者: Notarnicola, Ivano; Simonetto, Andrea; Farina, Francesco; Notarstefano, Giuseppe
• 署名单位: University of Bologna; Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3147007
• 发表日期: 2023
• 页码: 588-595
• 关键词: Distributed learning; distributed optimization; online optimization

摘要

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: 1) a dynamic gradient tracking scheme for finding local solution estimates and 2) 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.