The Analytics of Robust Satisficing: Predict, Optimize, Satisfice, then Fortify

Abstract

We introduce a novel approach to prescriptive analytics that leverages robust satisficing techniques to determine optimal decisions in situations of risk ambiguity and prediction uncertainty. Our decision model relies on a reward function that incorporates uncertain parameters, which can be partially predicted using available side information. However, the accuracy of the linear prediction model depends on the quality of regression coefficient estimates derived from the available data. To achieve a desired level of fragility, we begin by establishing a target relative to the predict-then-optimize objective and solve a residual-based robust satisficing model. Next, we solve a new estimation-fortified robust satisficing model that minimizes the influence of estimation uncertainty while ensuring that the estimated fragility of the solution in achieving a less ambitious guarding target falls below the level for the desired target. Our approach is supported by statistical justifications, and we propose tractable models for various scenarios, such as saddle functions, two-stage linear optimization problems, and decision-dependent predictions. We demonstrate the effectiveness of our approach through case studies involving a wine portfolio investment problem and a multi-product pricing problem using real-world data. Our numerical studies show that our approach outperforms the predict-then-optimize approach in achieving higher expected rewards when evaluated on the actual distribution. Notably, we observe significant improvements over the benchmarks, particularly in cases of limited data availability.

Keywords: Robust optimization, robust satisficing, predictive analytics, prescriptive analytics