Title: Sparsity in Distributionally Robust Optimization
Speaker: Dr. Divya Padmanabhan, Singapore University of Technology and Design (SUTD)
Date & Time: Wednesday, 19th February 2020 at 11 AM
Venue: IEOR Teaching Lab (Room. 011, Ground Floor, IEOR Building)
Abstract:
The theory of optimization has been central to solving decision problems in several applications ranging from operations research to machine learning. In solving such optimization problems, the parameters (for example, the objective coefficients in linear programs) have assumed to be known traditionally. However, many a time, the parameters of the optimization problem are prone to errors or are random; unfortunately, a small change in the parameters greatly impacts the optimal decisions. Distributional robust optimization (DRO) is a field that aims at handling randomness in the objective function and/or constraints of optimization problems. In typical applications, some information is available about the underlying probability distribution governing the random parameters while the complete distribution is itself unknown. The known information induces a class of consistent distributions (e.g moment based ambiguity, Wasserstein distance-based ambiguity, etc). Distributionally robust variants then look at obtaining the best decisions for the worst-case expected objective value over this class. In several cases, the DRO variants are known to be NP-hard.
In this talk, I will first introduce the concept of DRO through applications, for the benefit of those new to the area. I will primarily talk of our contributions in (1) moment based ambiguity sets (2) marginal distribution based ambiguity sets. Though the ambiguity sets are fundamentally different, we show that sparsity in the provided information plays a role in obtaining polynomial sized reformulations. The specific techniques for deriving reformulations differ based on the ambiguity set and objective under consideration. The reformulations that I will present in the talk are based on semi-definite programming and linear programming approaches.
About the Speaker:
Dr. Divya Padmanabhan is a post-doctoral researcher at the Singapore University of Technology and Design (SUTD). She received her Ph.D. from the Dept. of Computer Science and Automation at the Indian Institute of Science (IISc), Bangalore, MTech and BTech in CSE from IIT Madras and NIT Calicut respectively. In the past, she has worked on several diverse problems spanning machine learning, game theory and computational biology. She is currently working on distributionally robust optimization. She has industry experience in Oracle and has also been a research intern at IBM IRL and Xerox Research Centre India (now Conduent).