Integrated Machine Learning and Optimization for Data-Driven Decision-Making
In real-world decision problems, the presence of uncertainty in the multiple parameters that model either the objective function to be optimized (e.g., minimizing travel times) or some of the constraints that must be satisfied (e.g., demands) is the usual scenario. In Robust Optimization, we deal with a collection of problems of a common structure but with the parameters of the model varying in some uncertainty set. We study an approach to build these uncertainty sets by leveraging the contextual information provided by a set of covariates (e.g., weather). Specifically, we design ellipsoidal uncertainty sets that are defined by the maximum likelihood estimated parameters of the assumed Gaussian distribution resulting from conditioning the uncertain parameters to the given values of the covariates, and provide both theoretical and empirical guarantees for the coverage provided. Finally, we implement our approach to demonstrate the value of exploiting contextual information.
Palabras clave: Robust optimization Data Decision Driving Neural Networks