# Distributed learning and optimization with non-stationary data streams

### Tao Li – School of Mathematical Sciences, East China Normal University, Chine

We study the decentralized online linear regression 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 L2 regularization term. 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. We also consider the distributed stochastic subgradient optimization algorithm with noisy measurements of local cost functions' subgradients, additive and multiplicative noises among information exchanging between each pair of nodes, and we prove that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected, then proper algorithm step sizes can be designed so that all nodes' states converge to the global optimal solution almost surely.

Biography: Tao Li received the B.E. degree in automation from Nankai University, Tianjin, China, in 2004, and the Ph.D. degree in systems theory from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China, in 2009. Since January 2017, he has been with East China Normal University, Shanghai, China, where he is currently the Chang Jiang Distinguished Professor in Operations Research and Cybernetics, the Vice Director of the Key Laboratory of Mathematics and Engineering Applications, Ministry of Education, China, and an affiliated professor of the Institute of Mathematical Sciences of New York University at Shanghai. His current research interests include stochastic systems, cyber-physical multiagent systems, distributed algorithms, and game theory.

Dr. Li was a recipient of the 28th Zhang Siying Outstanding Youth Paper Award in 2016, the Best Paper Award of the 7th Asian Control Conference in 2009, and honorable mentioned as one of finalists for the Young Author Prize of the 17th IFAC Congress in 2008. He received the 2009 Singapore Millennium Foundation Research Fellowship and the 2010 Australian Endeavor Research Fellowship. He was entitled Dongfang Distinguished Professor by Shanghai Municipality in 2012, received the Excellent Young Scholar Fund from NSFC in 2015. He was twice elected to the Chang Jiang Scholars Program, Ministry of Education, China (Youth Scholar in 2018 and Distinguished Professor in 2023). He now serves as Associate Editor for several journals, including Systems and Control Letters, IFAC Nonlinear Analysis: Hybrid Systems, IEEE Control Systems Letters and SCIENCE CHINA Information Sciences. He is a Member of the IFAC Technical Committee 1.5 on Networked Systems and Senior member of IEEE.

### Lieu

CIM

Pavillon McConnell

Université McGill

Montréal QC H3A 0E9

Canada