报告题目：Sample Average Approximation for Conditional Stochastic Optimization with Dependent Data

报告人：孔令臣

报告时间：2024年10月05日（周六）08:30开始

报告地点：数学楼315会议室

报告摘要：Conditional Stochastic Optimization (CSO) is a powerful modelling paradigm for optimization under uncertainty. The existing literature on CSO is mainly based on the independence assumption of data, which shows that the solution of CSO is asymptotically consistent and enjoys a finite sample guarantee. The independence assumption, however, does not typically hold in many important applications with dependence patterns, such as time series analysis, operational control, an dreinforcement learning. In this paper, we aim to fill this gap and consider a Sample Average Approximation (SAA) for CSO with dependent data. Leveraging covariance inequalities and independent block sampling technique, we provide theoretical guarantees of SAA for CSO with dependent data. In particular, we show that SAA for CSO retains asymptotic consistency and a finite sample guarantee under mild conditions. In addition, we establish the sample complexity O(d/ε 4)of SAA for CSO, which is shown to be of the same order as independent cases. Through experiments on several applications, we verify the theoretical results and demonstrate that dependence does not degrade the performance of the SAA approach in real data applications.

报告人简介：孔令臣，教授，博士生导师，中国运筹学会数学规划分会理事长，北京交通大学数学与统计学院副院长。主要从事对称锥互补问题和最优化、高维数据分析、统计优化与学习、医学成像等方面的研究,发表论文60余篇。主持国家自然科学基金面上项目4项和专项基金项目4项, 参与国家自然科学基金重点项目、重点研发项目以及973课题等。2005年获山东省高等教育教学成果三等奖，2012年获中国运筹学会青年奖，2018年获得北京市高等教育教学成果一等奖，2022年获教育部自然科学二等奖和北京市高等教育教学成果二等奖。