Task-Based Prescriptive Trees for Two-Stage Linear Decision-Making Problems

Most decision-making problems are framed as two-stage stochastic programs. The standard framework follows a sequential two-step process: a predictive distribution is firstly estimated, leveraging on machine-/statistical-learning (M/SL) methods; then, a decision is prescribed by solving the two-stage stochastic program using the estimated distribution. M/SL methods typically focus only on minimizing the uncertain parameters prediction error, leaving out the impact on the decision problem. However, practitioners' main interest is to obtain prescriptions under uncertainty with minimum decision error rather than decisions oriented by least-error predictions. In this work, we propose a new framework where the M/SL training function also accounts for the downstream optimization problem. We focus on decision trees, presenting an exact non-convex mathematical programming-based formulation and also a recursive-partitioning heuristic strategy to identify good and feasible solutions to the non-convex problem. Finally, we analyze a set of experiments illustrating the effectiveness of the proposed methodology, benchmarking against standard frameworks.