We propose a new robust explainable prescriptive analytics framework that minimizes a risk-based objective function under distributional ambiguity by leveraging the data collected on the past realizations of the uncertain parameters affecting the decision model and the side information that have some predictive power on those uncertainties. The framework solves for an explainable response policy that transforms the side information directly to implementable here-and-now decisions. Such a policy should endow with the properties of facilitating explanation of the decisions, ensuring that the solutions are implementable, and maintaining the computational tractability of the optimization problem. We show that affine and tree-based policies could achieve these salient properties. Although the historical data is available, the data-generating probability distribution remains unobservable. Hence, we adopt the data-driven robust satisficing framework to address the issue of overfitting when the empirical distribution is used for evaluating the risk-based objective function. We also propose a localized robust satisficing model, which can be applied to solving combinatorial optimization problems efficiently for a tree-based static policy. To address linear optimization models with recourse, we provide a new safe tractable approximation that ensures the feasibility of the robust satisficing model, which can deal with constraints that are biaffine in the outcome variables and the side information. We also introduce a new biaffine recourse adaptation to improve the quality of the approximation. We provide a simulation case study on how the framework can be applied to in a risk minimizing portfolio optimization problem using past returns as side information.
This is joint work with Li Chen, Xun Zhang, Long Zhao and Minglong Zhou.