Title: Data-Driven Sample-Average Approximation for Stochastic Optimization with Covariate Information
|Affiliation:||University of Wisconsin-Madison|
|Zoom:||Please email Emma Watson|
We consider optimization models for decision-making in which parameters within the optimization model are uncertain, but predictions of these parameters can be made using available covariate information. We consider a data-driven setting in which we have observations of the uncertain parameters together with concurrently-observed covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate a data-driven framework in which the outputs from a machine learning prediction model are directly used to define a stochastic programming sample average approximation (SAA). The framework is flexible and accommodates parametric, nonparametric, and semiparametric regression techniques. The basic version of this framework is not new, but we are the first to analyze the procedure and derive conditions on the data generation process, the prediction model, and the stochastic program under which solutions of these data-driven SAAs are consistent and asymptotically optimal. We also derive convergence rates and finite sample guarantees. We also propose new variations that use out-of-sample residuals of leave-one-out prediction models for scenario generation. Computational experiments validate our theoretical results, demonstrate the potential advantages of our data-driven formulations over existing approaches (even when the prediction model is misspecified), and illustrate the benefits of our new variants in the limited data regime.
Coauthors: Rohit Kannan (U. Wisconsin-Madison) and Guzin Bayraksan (Ohio State)