报告题目：Linear convergence of proximal descent schemes on the Wasserstein space
时 间：2025年12月08日（星期一）14：30
地 点：理工南楼621
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：In this talk, I will discuss proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space. I will explain how to establish linear convergence under flat convexity assumptions, thereby relaxing the common reliance on geodesic convexity. The analysis circumvents the need for discrete-time adaptations of the Evolution Variational Inequality (EVI). Instead, we can leverage a uniform logarithmic Sobolev inequality (LSI) and the entropy sandwich lemma. The major challenge in the proof via LSI is to show that the relative Fisher information is well-defined at every step of the scheme. Since the relative entropy is not Wasserstein differentiable, we prove that along the scheme the iterates belong to a certain class of Sobolev regularity, and hence the relative entropy has a unique Wasserstein sub-gradient, and that the relative Fisher information is indeed finite. The talk is based on joint work with Razvan-Andrei Lascu (RIKEN), David Siska (University of Edinburgh) and Lukasz Szpruch (University of Edinburgh).
报告人简介：Mateusz B. Majka is affiliated with Heriot-Watt University, UK, with an email at mateusz.b.majka@gmail.com and a website at https://sites.google.com/site/mateuszbmajka/; his research interests include stochastic differential equations, mathematical foundations of machine learning (such as stochastic gradient algorithms and mean-field optimization), computational statistics, Lévy processes, and ergodicity of Markov processes. He earned a PhD in Mathematics from the University of Bonn, Germany, in 2017 (thesis: “Stability of Stochastic Differential Equations with Jumps by the Coupling Method”), an MSc in Financial Mathematics from Jagiellonian University, Krakow, Poland, in 2012, and a BSc in Mathematics from the same university in 2010. Professionally, he has been an Assistant Professor at Heriot-Watt University, Edinburgh, UK, since 2020, a Research Fellow at the University of Warwick, UK, from 2018 to 2020, and a Research Associate at King’s College London, UK, from 2017 to 2018. He has supervised 2 PhD students, published work in journals like Bernoulli and Stochastic Processes and their Applications, organized stochastic analysis workshops, and served as Programme Director of BSc Data Sciences at Heriot-Watt University.