The Analytics of Robust Satisficing

We propose a new prescriptive analytics model based on robust satisficing that incorporates a prediction model to determine the here-and-now decision that would achieve a target expected reward as well as possible under both risk ambiguity and estimation uncertainty. The reward function of the decision model depends on some observable parameters whose future realizations are uncertain, and their outcomes may be influenced by some observable factors or the decision made. The robust satisficing model features a em residual ambiguity set that characterizes the risk ambiguity of the regression residuals via a moment constraint on the expected prediction loss, and a {\em regularized estimation set} that characterizes the estimation uncertainty of the regression coefficients imposed by a regularization constraint. We provide statistical justification for the robust satisficing models and formulate tractable models when the reward function is a saddle function. We feature two applications and use real data in their case studies; a wine portfolio investment problem, and a multi-product pricing problem. Through these numerical studies, we elucidate the benefits of our robust satisficing model over the predict-then-optimize approach; when evaluated on the true distribution, the robust satisficing models yield solutions with lower risks, and with suitably chosen targets, they could also achieve higher expected reward. We observe consistent and significant improvement over the benchmarks, and the improvements are more pronounced when less data is available