报告地点：腾讯会议907976429
邀请人：孙海琳教授
Abstract: In recent years, there is a growing interest of nonconvex, nonsmooth and nondeterministic optimization problems. In the first part of this talk, we focus on a class of nonconvex and nonsmooth stochastic optimization problems with implicitly decision-dependent uncertainty. The dependency between the uncertainty and the decision variable is unknown, but could be predicted through the observational data pairs. In order to balance the trade-off between the prediction accuracy and the complexity of optimization problems, we propose an algorithm that couples learning and optimization based on trust region methods. We show that the sequence of solutions converges to a directional stationary solution with probability 1. In the second part, we focus on the nonconvex piecewise affine regression when the training data is contaminated by outliers. We propose a risk-based robust regression model so that the outliers are automatically removed in model fitting. We develop a stochastic difference-of-convex algorithm to asymptotically compute a critical solution to the original parameter estimation problem with probability 1. Numerical experiments show that this risk-based robust regression model yields significantly smaller mean absolute errors on the validation data set compared with the ordinary least square estimator and classical robust regression estimators.
报告人简介: 刘俊驿博士，清华大学工业工程系助理教授，2015年于中国科学技术大学少年班*女王调教-女王调教视频-女王 调教小说获得统计学本科学位，2019年于美国南加州大学工业与系统工程系获得博士学位。2019年9月至2021年3月在南加州大学Prof. Jong-Shi Pang的指导下做博士后研究。研究领域聚焦在非凸非平滑的随机优化及其在统计、机器学习、风险管理等方向的交叉应用。在SIAM Journal on Optimization、Mathematics of Operations Research国际权威期刊发表了多篇论文。
Speaker Bio: Junyi Liu is currently an assistant professor at the Department of Industrial Engineering at Tsinghua University. She obtained the Ph.D. degree in Industrial and Systems Engineering at the University of Southern California at 2019, and the B.S. degree in Statistics in the School of Gifted Young at the University of Science and Technology of China at 2015. She was a postdoctoral researcher working with Prof. Jong-Shi Pang from Sep 2019 till March 2021. Her research interests lie into the intersections of nonconvex and nonsmooth stochastic optimization with machine learning and statistics. She has published several papers in top journals such as SIAM Journal on Optimization, and Mathematics of Operations Research.