主办人：孔令臣、严明、江如俊等

主办单位：数学与大数据学院

论坛时间：2023年11月3日—5日

论坛地点：柏天酒店

大会报告1: Study on Differential Privacy Learning in Regression and Clustering

内容简介：Statistical machine learning technology has rapidly developed and made significant breakthroughs in application fields. However, an attacker's intrusion can easily disrupt the learning process, leading to the system becoming unreliable. For example, in the field of precision medicine, attacks can lead to serious side effects in patients' treatment plans and leak their personal information. Trustworthy machine learning has gradually become a new and popular research direction in artificial intelligence, committed to making machine learning and trustworthy, including security, robustness, privacy, fairness, and interpretability. At present, privacy-preserving is gradually receiving attention and attention from experts and scholars in fields such as machine learning and statistics. Considering that regression and clustering are the fundamental positions of machine learning methods, this report will briefly outline the research progress of differential privacy techniques in regression and clustering, and introduce our new noise mechanism proposed in distributed learning to achieve privacy protection.

主讲人简介：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、稀疏优化、低秩矩阵优化、高维数据聚类、矩阵回归、统计优化与学习、医学成像等方面的研究。在《Mathematical Programming》《SIAM Journal on Optimization》《IEEE Transactions on Pattern Analysis and Machine Intelligence》《IEEE Transactions on Signal Processing》《Technometrics》《Statistica Sinica》《Electronic Journal of Statistics》等期刊发表论文60余篇。主持国家自然科学基金面上项目“高维稳健隐私回归的优化模型理论与算法研究”“高维聚类的结构矩阵优化理论与算法”、“高维约束矩阵回归的优化理论与算法”、“矩阵秩极小问题的松弛理论与算法研究”和专项项目“统计优化与人工智能天元数学交流项目”等, 参与重点项目“大规模稀疏优化问题的理论与算法”以及973课题等。曾获中国运筹学会青年奖，教育部自然科学二等奖和北京市高等教育教学成果一等奖等。

大会报告2: 带压缩的分布式优化算法

内容简介：分布式优化在解决大规模问题和处理分布式数据方面起着关键作用，但节点之间数据传输问题成为新的瓶颈。数据传输压缩是有效应对低带宽的一项关键策略，它有助于缩短总通信时间。然而，数据压缩也引入了新的误差，为算法设计带来了新的挑战。本报告将介绍一系列方法，用以降低分布式优化中压缩误差的影响。这些方法能够有效减少或甚至消除压缩误差，使算法在稍微增加计算时间的情况下，显著减少通信时间。

主讲人简介：严明，香港中文大学（深圳）数据科学学院副教授。2005年和2008年分别获得中国科学技术大学数学学士和硕士学位，2012年获得加州大学洛杉矶分校的数学博士学位。研究兴趣包括优化及其在图像处理、机器学习和其他数据科学问题中的应用。先后在莱斯大学和加州大学洛杉矶分校担任博士后研究员。2015-2022年在密歇根州立大学计算数学、科学和工程系和数学系担任助理教授和副教授。2020年获得Facebook教授奖。自2021年起连续入选“全球前2%顶尖科学家“榜单。

大会报告3：Decision Making under Cumulative Prospect Theory: An Alternating Direction Method of Multipliers

内容简介: In this talk, I will present a novel numerical method for solving the problem of decision making under cumulative prospect theory (CPT), where the goal is to maximize utility subject to practical constraints, assuming only finite realizations of the associated distribution are available. Existing methods for CPT optimization rely on particular assumptions that may not hold in practice. To overcome this limitation, we present the first numerical method with a theoretical guarantee for solving CPT optimization using an alternating direction method of multipliers (ADMM). One of its subproblems involves optimization with the CPT utility subject to a chain constraint, which presents a significant challenge. To address this, we develop two methods for solving this subproblem. The first method uses dynamic programming, while the second method is a modified version of the pooling-adjacent-violators algorithm that incorporates the CPT utility function. Moreover, we prove the theoretical convergence of our proposed ADMM method and the two subproblem-solving methods. Finally, we conduct numerical experiments to validate our proposed approach and demonstrate how CPT's parameters influence investor behavior using real-world data. I will also talk about an application of the algorithm to rank-based loss minimization in machine learning.

主讲人简介：江如俊，复旦大学大数据学院副教授，博士生导师。2016年7月于香港中文大学获得博士学位。研究方向主要包括优化算法和理论分析，二次规划及其在运筹学、机器学习和金融工程领域的应用。其研究成果发表在Math.Program.,SIAM J.Optim. 、Math.Oper.Res.、INFORMS J.Comput.和ICML等国际顶级期刊或会议上。获上海市扬帆计划、国家级青年人才计划支持。主持国家自然科学基金青年项目和面上项目。曾获国际机器学习大会ICML2022杰出论文奖。

附件：第九届（2023年）中国运筹学会数学规划分会研究生论坛分组报告