Exploring the Sparsity of Large-scale Statistical Optimization Problems
发布时间：2022年11月01日
浏览次数：3228
发布者: Wenqiong Li
主讲人： 孙德锋 （香港理工大学）
活动时间： 从 2022-11-08 16:00 到 17:00
场地： 线上
Abstract: It has been widely recognized that the structured sparsity of the optimal solutions is an intrinsic property for large-scale optimization problems arising from modern applications in the big data era. In this talk, we shall first illustrate the structured sparsity of the solutions via some popular machine learning models. In particular, we shall show that the solution of the convex clustering model can be highly structurally sparse even if the solution itself is fully dense. We shall then introduce a dual semismooth Newton based proximal point algorithm (PPDNA) and use nonsmooth analysis to explain why it can be much more efficient than the first-order methods for solving a class of large-scale optimization problems arising from machine learning. The key point is to adaptively make use of the second-order sparsity of the solutions in addition to the data sparsity so that, at each iteration, the computational costs of the second-order methods can be comparable or even lower than those of the first-order methods. Equipped with the PPDNA, we shall then introduce some adaptive sieving methodologies to generate solution paths for large-scale optimization problems with structured sparsity of particular importance in applications. In the last part of the talk, we shall illustrate the high efficiency of our approach with extensive numerical results on several important models including convex clustering, lasso, and exclusive lasso.
Speaker: Professor Defeng Sun is currently Chair Professor of Applied Optimization and Operations Research at the Hong Kong Polytechnic University and the President of the Hong Kong Mathematical Society. He mainly publishes in non-convex continuous optimization and machine learning. Together with Professor Kim-Chuan Toh and Dr Liuqin Yang, he was awarded the triennial 2018 Beale--Orchard-Hays Prize for Excellence in Computational Mathematical Programming by the Mathematical Optimization Society. He served as editor-in-chief of Asia-Pacific Journal of Operational Research from 2011 to 2013 and he now serves as associate editor of Mathematical Programming, SIAM Journal on Optimization, Journal of Optimization Theory and Applications, Journal of the Operations Research Society of China, Journal of Computational Mathematics, and Science China: Mathematics. In 2020, he was elected as a Fellow of the societies CSIAM and SIAM and in 2021 he has received the Distinguished Collaborator Award from both the Hong Kong Research Center and Huawei Noah's Ark Lab, Huawei Technologies Co. Ltd. for the contributions on developing efficient and robust techniques for solving huge scale linear programming models arising from production planning and supply chain logistics. In 2022, he received the RGC Senior Research Fellow Scheme award.
Tencent Meeting:
https://meeting.tencent.com/dm/w1sUqKzPwowi
ID: 762-502-595
