【报告摘要】We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of a random Tikhonov regularization path and decompose the tracking error of the algorithm’s output for the regularization path into random difference equations in RKHS. We show that the tracking error vanishes in mean square and almost surely if the regularization path is slowly time-varying. Then, leveraging the monotonicity of inverse operators and the spectral decomposition of compact operators, and introducing the RKHS persistence of excitation condition, we develop a dominated convergence method to prove the mean square and almost sure consistency between the regularization path and the unknown function to be learned. Especially, for independent and non-identically distributed data streams, the mean square and almost sure consistency between the algorithm’s output and the unknown function is achieved if the input data’s marginal probability measures are slowly time-varying and the average measure over each fixed-length time period is uniformly above a strictly positive finite Borel measure.

【报告人简介】李韬，系统科学研究所研究员，2004年本科毕业于南开大学自动化专业，2009年获中国科学院数学与系统科学研究院系统理论博士学位。曾入选中国科学院青年创新促进会首批会员(2011)、上海市“东方学者”特聘教授(2012)和教育部“长江学者奖励计划”特聘教授(2022)。主要研究方向为随机系统与控制、分布式学习、控制与博弈、能源系统管理与调控等。曾主持国家自然科学基金优秀青年科学基金(2016-2018)、中俄(NSFC-RSF)联合基金。曾获第7届亚洲控制会议最佳论文、第28届张嗣瀛优秀青年论文、新加坡千禧基金研究奖、澳大利亚教育部奋进研究奖、中国科学院院长特别奖等。担任 IEEE Transactions on Automatic Control、Systems and Control Letters、Nonlinear Analysis: Hybrid Systems、SCIENCE CHINA Information Sciences等期刊的责任编委等。