HKU IDS Scholar Seminar Series #27:
Robust Data-Driven Quasi-concave Optimization
Abstract
We investigate a data-driven quasiconcave maximization problem where information about the objective function is limited to a finite sample of data points. We begin by defining an ambiguity set for admissible objective functions based on available partial information about the objective. This ambiguity set consists of those quasiconcave functions that majorize a given data sample, and that satisfy additional functional properties (monotonicity, Lipschitz continuity, and permutation invariance). We then formulate a robust optimization (RO) problem which maximizes the worst-case objective function over this ambiguity set. Based on the quasiconcave structure in this problem, we explicitly construct the upper level sets of the worst-case objective at all levels. We can then solve the resulting RO problem efficiently by doing binary search over the upper level sets and solving a logarithmic number of convex feasibility problems. This numerical approach differs from traditional subgradient descent and support function based methods for this problem class. While these methods can be applied in our setting, the binary search method displays superb finite convergence to the global optimum, whereas the others do not. This is primarily because binary search fully exploits the specific structure of the worst-case quasiconcave objective, which leads to an explicit and general convergence rate in terms of the number of convex optimization problems to be solved. Our numerical experiments on a Cobb-Douglas production efficiency problem and a fair resource allocation problem demonstrate the tractability of our approach.
Publication Note
This seminar is based on Prof Qingpeng ZHANG’s recent publication in PNAS, with Dr Fei JING—his Postdoctoral Fellow at IDS—as first author. Prof ZHANG will give a detailed account of the paper and its theoretical framework for understanding the predictability limits of complex systems.
Speaker
Dr. Wenjie Huang
Research Assistant Professor @ HKU IDS & Department of Data and Systems Engineering
Dr. Wenjie Huang is Research Assistant Professor in Department of Data and Systems Engineering and Musketeers Foundation Institute of Data Science, The University of Hong Kong (HKU), recruited by HKU-100 Global Recruitment Exercise.
He received B.S. degree in Industrial Engineering and Management, with minor in Economics, from Shanghai Jiao Tong University in 2014, and then Ph.D. degree in Industrial Systems Engineering and Management, from National University of Singapore in 2019, supervised by William B. Haskell and Tang Loon Ching. Prior to joining HKU, he held joint postdoc positions at School of Data Science, The Chinese University of Hong Kong, and Department of Decision Sciences, HEC Montréal, Québec, Canada (also affiliated with Shenzhen Research Institute of Big Data and Group for Research in Decision Analysis (GERAD)), from Sep 2019 to Sep 2021, working with Prof. Erick Delage and Prof. Zizhuo Wang.
He has been acting as the role of PI/Co-PI/Co-I for Hong Kong RGC (GRF and Theme-Based) funds and NSFC (Young Scientist-Type C, General, and Original Exploration) funds. His research was selected as Finalists of 2025 IEEE CASE Best Application Paper Award, feature article by IEEE CSS-DES Newsletter, and presentation at INFORMS MSOM Conference. He is an ad-hoc reviewer/programme committee member for several top journals and conferences including: Operations Research, Journal of Machine Learning Research, IEEE Transactions on Automatic Control, INFORMS Journal on Computing, Production and Operations Management, AAAI, UAI, and IEEE CDC.
For full biography of Dr. Huang, please refer to: https://datascience.hku.hk/people/wenjie-huang/
Moderator
Dr Yue XIE
Research Assistant Professor @ HKU IDS & Department of Mathematics
Dr Yue XIE is a Research Assistant Professor in the Musketeers Foundation Institute of Data Science and the Department of Mathematics at The University of Hong Kong. He was previously a postdoctoral researcher at UW-Madison, working in the nonconvex optimisation group led by Professor Stephen J. Wright. He received his PhD from Pennsylvania State University and his bachelor’s degree from Tsinghua University.
Dr Xie focuses on algorithm design and analysis for nonconvex and stochastic optimisation problems, with applications in machine learning and data science. He has published in, and served as a referee for, leading journals including Mathematical Programming, SIAM Journal on Optimization, and IEEE Transactions on Automatic Control. He has also delivered presentations at major international conferences including ICCOPT, ISMP, the SIAM Conference on Optimization, and ICML.
For full biography of Dr. Xie, please refer to: https://datascience.hku.hk/people/yue-xie/
