Season 6 

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 an alternative, and often computationally advantageous approach, based on learning. Our method parametrizes the solution map within a given function class and solves a single stochastic optimization problem. When using constant step-size stochastic gradient descent, 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 even stronger results for the learning approach that demonstrate complexity improvements over the best known results for uniform discretization. We complement our theoretical results with evidence of strong numerical performance on imbalanced binary classification and portfolio optimization examples. Time permitting, we discuss some extensions and related work on parametric constrained robust optimization problems.

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.

In this talk we discuss several approaches to the formulation of distributionally robust counterparts of Markov Decision Processes,  where the transition kernels are not specified exactly but rather are assumed to be elements of the corresponding ambiguity sets.  The intent is to clarify some connections between the game and static formulations of distributionally robust MDPs,  and explain the role of rectangularity associated with ambiguity sets in determining these connections.

Alexander Shapiro is the A. Russell Chandler III Chair and Professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. In 2013 he was awarded Khachiyan Prize of INFORMS for lifetime achievements in optimization, and in 2018 he was a recipient of the Dantzig Prize awarded by the Mathematical Optimization Society and Society for Industrial and Applied Mathematics.  In 2020 he was elected to the National Academy of Engineering. In 2021 he was a recipient of John von Neumann Theory Prize awarded by INFORMS.