Title: Protection at All Levels: Probabilistic Envelope Constraints
Speaker: Dr. Xu Huan
Affiliation: Department of Mechanical Engineering at National University of Singapore
Location: CPSE Seminar room (C616 Roderic Hill)
Time: 2:00pm
Abstract. Optimization under chance constraints is a standard approach to ensure that bad events such as portfolio losses, are unlikely to happen. They do nothing, however, to protect more against terrible events (e.g., deep portfolio losses, or bankruptcy). In this talk, we will propose a new decision concept, termed "probabilistic envelop constraint", which extends the notion of chance constraints, to a formulation that provides different probabilistic guarantees at each level of constraint violation. Thus, we develop a notion of guarantee across the spectrum of disasters, or rare events, ensuring these levels of protection hold across the curve, literally. We further show that the corresponding optimization problem can be reformulated as a semi-infinite optimization problem, and provide conditions that guarantee its tractability. Interestingly, the resulting formulation is what is known as a comprehensive robust optimization in literature. This work thus provides a new fundamental link between two main methodologies in optimization under uncertainty: stochastic optimization and robust optimization. This is a joint work with Constantine Caramanis (UT-Austin) and Shie Mannor (Technion).
About the speaker. Huan Xu has been an assistant professor of Mechanical Engineering of National University of Singapore since 2011. He obtained his Ph. D. degree in ECE from McGill University, Canada, in 2009, and was a postdoctral research fellow of the University of Texas at Austin prior to joining NUS. His current research interest focuses on learning and decision-making in large-scale complex systems, including machine learning, high-dimensional statistics, robust and adaptable optimization, robust sequential decision making, and applications to large-scale systems. He has published in leading operations research and machine learning journals including Operations Research, Math. Oper. Res., IEEE Info. Theory, JMLR, and conferences including ICML, NIPS, and COLT.