Decentralized Online Regularized Learning Over Random Time-Varying Graphs

• 成果类型: Article
• 署名作者: Zhang, Xiwei; Li, Tao; Fu, Xiaozheng
• 署名单位: East China Normal University; East China Normal University; Chinese Academy of Sciences; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Ningbo University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3563542
• 发表日期: 2025
• 页码: 6609-6624
• 关键词: estimation; Linear Regression; mathematical models; Symmetric matrices; noise; vectors; estimation error; Technological innovation; Noise measurement; CONVERGENCE; Decentralized online linear regression; random time-varying graph; Regret Analysis; regularization; persistence of excitation

摘要

We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new measurement, a consensus term taking a weighted sum of estimations of its own and its neighbors with additive and multiplicative communication noises and a regularization term preventing over-fitting. It is not required that the regression matrices and graphs satisfy special statistical assumptions such as mutual independence, spatio-temporal independence or stationarity. We develop the nonnegative supermartingale inequality of the estimation error, and prove that the estimations of all nodes converge to the unknown true parameter vector almost surely if the algorithm gains, graphs and regression matrices jointly satisfy the sample path spatio-temporal persistence of excitation condition. Especially, this condition holds by choosing appropriate algorithm gains if the graphs are uniformly conditionally jointly connected and conditionally balanced, and the regression models of all nodes are uniformly conditionally spatio-temporally jointly observable, under which the algorithm converges in mean square and almost surely. In addition, we prove that the regret upper bound is O(T(1-tau )ln T), where tau is an element of (0.5,1) is a constant depending on the algorithm gains.