题　目：An error bound-based convergence analysis framework for a class of randomized algorithms

嘉　宾：余文忠，副教授，香港理工大学

主持人：刘慧康，副教授，上海交通大学安泰经济与管理学院

时　间：2026年4月27日（周一）14:00-15:30

地　点：上海交通大学徐汇校区安泰浩然楼308室

内容简介:

Existing error-bound-based analyses for stochastic algorithms that exhibit certain descent properties, such as randomized coordinate descent and randomized projection methods, are often limited in scope and typically lead to overly conservative convergence guarantees. To address this gap, we develop an abstract framework for analyzing such stochastic algorithms based on new unified error bound (UEB) conditions. The proposed UEB conditions subsume many common error bound- and Kurdyka–Łojasiewicz-type conditions used in existing studies of algorithms for optimization, convex feasibility, and common fixed point problems. Under the global UEB condition, we establish non-asymptotic in-expectation and asymptotic almost-sure convergence rates for the stochastic algorithms in our framework. Under the local UEB condition, we also show asymptotic almost sure convergence rates. We demonstrate the strength and versatility of our framework through two applications. For the common fixed point problem, we provide comprehensive convergence guarantees for the randomized alternating Krasnoselskii-Mann method under Hölderian error bound conditions. Furthermore, for unconstrained minimization of smooth definable functions, we establish novel convergence guarantees for the randomized subspace descent method, an algorithm subsuming both randomized coordinate and block coordinate descent.

演讲人简介：

Dr. Man-Chung Yue is currently an Associate Professor at the Department of Applied Mathematics of The Hong Kong Polytechnic University. He received his B.Sc. degree in Mathematics and Ph.D. degree in Systems Engineering and Engineering Management, both from The Chinese University of Hong Kong. He also worked at The University of Hong Kong as an Assistant Professor and Imperial College London as a Research Associate. His research focuses on continuous optimization and its interplay with decision-making under uncertainty, signal processing, machine learning, and operations research. 

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