Solving contextual stochastic optimization problems through contextual distribution estimation

Abstract

Stochastic optimization models always assume known probability distributions about uncertain parameters. However, it is unrealistic to know the true distributions. In the era of big data, with the knowledge of informative features related to uncertain parameters, this study aims to estimate the conditional distributions of uncertain parameters directly and solve the resulting contextual stochastic optimization problem by using a set of realizations drawn from estimated distributions, which is called the contextual distribution estimation method. We use an energy scheduling problem as the case study and conduct numerical experiments with real-world data. The results demonstrate that the proposed contextual distribution estimation method offers specific benefits in particular scenarios, resulting in improved decisions. This study contributes to the literature on contextual stochastic optimization problems by introducing the contextual distribution estimation method, which holds practical significance for addressing data-driven uncertain decision problems.