CORS / Optimization Days
HEC Montréal, May 29-31, 2023
CORS-JOPT2023
HEC Montreal, 29 — 31 May 2023
CONOI Contextual Optimization I
May 30, 2023 10:30 AM – 12:10 PM
Location: Xerox Canada (yellow)
Chaired by Erick Delage
3 Presentations
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10:30 AM - 10:55 AM
A Review of Contextual Stochastic Optimization I: Sequential Learning and Optimization
Decision-making under uncertainty involves solving optimization problems with uncertain (unobservable) parameters that can affect the objective function and constraints. When certain auxiliary variables (covariates) correlated with the uncertain parameters are revealed before making a decision, one solves a contextual stochastic optimization (CSO) problem for some conditional distribution of the uncertain parameters given the covariates. Traditionally, CSO problems are solved by learning an estimator (point prediction or distribution) based on its predictive performance and then solving an optimization problem using the estimator. Recently, there has been a surge of interest in the operations research and machine learning community on integrating optimization and learning to tune prediction models based on their prescriptive performance. We survey the literature on decision-focused learning models and discuss the challenges and open problems that can help us better understand the value of integrating optimization and machine learning.
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10:55 AM - 11:20 AM
A Review of Contextual Stochastic Optimization II: Integrated Learning and Optimization
Decision-making under uncertainty involves solving optimization problems with uncertain (unobservable) parameters that can affect the objective function and constraints. When certain auxiliary variables (covariates) correlated with the uncertain parameters are revealed before making a decision, one solves a contextual stochastic optimization (CSO) problem for some conditional distribution of the uncertain parameters given the covariates. Traditionally, CSO problems are solved by learning an estimator (point prediction or distribution) based on its predictive performance and then solving an optimization problem using the estimator. Recently, there has been a surge of interest in the operations research and machine learning community on integrating optimization and learning to tune prediction models based on their prescriptive performance. We survey the literature on decision-focused learning models and discuss the challenges and open problems that can help us better understand the value of integrating optimization and machine learning.
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11:20 AM - 11:45 AM
Robust Data-driven Prescriptiveness Optimization
The abundance of data has led to the emergence of a variety of optimization techniques, attempting to leverage the available side information to provide more anticipative decisions. Recent developments span a wide range of methods in the context of conditional optimization; on the other hand, the necessity of the existence of a universal unitless measure for the evaluation of different optimization schemes has given rise to the introduction of the coefficient of prescriptiveness, a two-folded metric for quantification of the quality of a data-driven decision compared to a reference decision as well as the prescriptiveness content of the side information. We introduce a distributionally robust conditional stochastic optimization model where the coefficient of prescriptiveness substitutes for the classical empirical risk minimization objective. We provide a convex optimization reformulation for this problem, demonstrate how it reduces to a linear program when a nested Conditional Value at Risk represents the ambiguity set, and provide a bisection method together with an acceleration scheme for tackling it. Studying a shortest path problem, we evaluate the robustness of the resulting policies against alternative methods when the out-of-sample dataset experiences a distribution shift.