AI4OPT Seminar Series
Date: Tuesday, May 20th, 12-1pm
Location: 9th floor Atrium in Coda Building (756 W Peachtree St NW, Atlanta, GA 30308)
Join Live Virtual: https://gatech.zoom.us/j/98131329313
Speaker: Paul Grigas
Parametric Optimization Beyond Discretization
Abstract: Many applications require solving a family of optimization problems, indexed by some hyperparameter vector, to obtain an entire solution map (or solution path in the case of a single hyperparameter). Traditional approaches proceed by discretizing and solving a series of optimization problems. This talk presents several alternative and computationally advantageous approaches. In the case of an unconstrained problem with arbitrary dependence on the hyperparameter in the objective, we propose a learning approach that parametrizes the solution map within a given function class and solves a single stochastic optimization problem. Our method offers substantial complexity improvements over discretization. When using constant step-size SGD, the uniform error of our learned solution map relative to the true map exhibits linear convergence to a constant that diminishes as the expressiveness of the function class increases. In the special case of a one-dimensional hyperparameter and under sufficient smoothness, we present two main sets of contributions: (i) stronger results for the learning approach that demonstrate complexity improvements over the best known results for uniform discretization, and (ii) alternative second-order algorithms and associated computational guarantees inspired by a differential equation perspective on the parametric solution path. We complement our theoretical results with evidence of strong numerical performance on imbalanced binary classification, moment matching, and portfolio optimization examples. Time permitting, we discuss some related work on parametric constrained robust optimization problems.
Bio: Paul Grigas is an associate professor of Industrial Engineering and Operations Research at the University of California, Berkeley. Paul’s research interests are broadly in optimization, machine learning, and data-driven decision-making, with particular emphasis on contextual stochastic optimization and algorithms at the interface of machine learning and continuous optimization. Paul’s research is funded by the National Science Foundation, and he is affiliated with the NSF Artificial Intelligence (AI) Research Institute for Advances in Optimization (AI4OPT). Paul was awarded 1st place in the 2020 INFORMS Junior Faculty Interest Group (JFIG) Paper Competition and the 2015 INFORMS Optimization Society Student Paper Prize. He received his B.S. in Operations Research and Information Engineering (ORIE) from Cornell University in 2011, and his Ph.D. in Operations Research from MIT in 2016.
Note: Lunch will be served at the seminar. So, please stop by 15 minutes before the seminar to pick up lunch.
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Videos of the past seminars can be seen on AI4OPT webpage at https://www.ai4opt.org/seminars/past-seminars
