Forecasting Outside the Box: Application-Driven Optimal Pointwise Forecasts for Stochastic Optimization

• URL: http://arxiv.org/abs/2411.03520v2
• Date: Fri, 08 Nov 2024 21:41:22 GMT
• Title: Forecasting Outside the Box: Application-Driven Optimal Pointwise Forecasts for Stochastic Optimization
• Authors: Tito Homem-de-Mello, Juan Valencia, Felipe Lagos, Guido Lagos,
• Abstract summary: We present an integrated learning and optimization procedure that yields the best approximation of an unknown situation. Numerical results conducted with inventory problems from the literature as well as a bike-sharing problem with real data demonstrate that the proposed approach performs well.
• Score: 0.0
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• Abstract: The exponential growth in data availability in recent years has led to new formulations of data-driven optimization problems. One such formulation is that of stochastic optimization problems with contextual information, where the goal is to optimize the expected value of a certain function given some contextual information (also called features) that accompany the main data of interest. The contextual information then allows for a better estimation of the quantity of interest via machine learning methods, thereby leading to better solutions. Oftentimes, however, machine learning methods yield just a pointwise estimate instead of an entire distribution. In this paper we show that, when the problem to be solved is a class of two-stage stochastic programs (namely, those with fixed recourse matrix and fixed costs), under mild assumptions the problem can be solved with just one scenario. While such a scenario - which does not have be unique - is usually unknown, we present an integrated learning and optimization procedure that yields the best approximation of that scenario within the modeler's pre-specified set of parameterized forecast functions. Numerical results conducted with inventory problems from the literature (with synthetic data) as well as a bike-sharing problem with real data demonstrate that the proposed approach performs well when compared to benchmark methods from the literature.

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