Bayesian Risk Optimization (BRO): A New Approach to Data-driven Stochastic Optimization

Wed, Dec 1, 2021, 4:30 pm
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Electrical and Computer Engineering
Center for Statistics and Machine Learning
CSML and ECE SEMINAR

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Abstract:

A large class of stochastic optimization problems involves optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the distributionally robust optimization (DRO), is to hedge against the worst case among an ambiguity set of candidate distributions. However, given that worst-case rarely happens, inappropriate construction of the ambiguity set can sometimes result in over-conservative solutions. To explore the middle ground between optimistically ignoring the distributional uncertainty and pessimistically fixating on the worst-case scenario, we propose a Bayesian risk optimization (BRO) framework for parametric underlying distributions, which is to optimize a risk functional applied to the posterior distribution of the unknown distribution parameter. Of our particular interest are four risk functionals: mean, mean-variance, value-at-risk, and conditional value-at-risk. To reveal the implication of BRO, we establish the consistency of objective functions and optimal solutions, as well as the asymptotic normality of objective functions and optimal values. We also extend the BRO framework to online and multi-stage settings.

Bio:

Enlu Zhou is currently an associate professor in the School of Industrial & Systems Engineering at Georgia Institute of Technology. She received the B.S. degree with highest honors in electrical engineering from Zhejiang University, China, in 2004, and the Ph.D. degree in electrical engineering from the University of Maryland, College Park, in 2009. Before joining Georgia Tech in 2013, she was an assistant professor in the Industrial & Enterprise Systems Engineering Department at the University of Illinois Urbana-Champaign from 2009-2013. She is a recipient of the Best Theoretical Paper award at the Winter Simulation Conference, AFOSR Young Investigator award, NSF CAREER award, and INFORMS Simulation Society Outstanding Publication award. She has served or is currently serving as an associate editor for Journal of Simulation, IEEE Transactions on Automatic Control, and Operations Research.