Orateur
Description
Decision-makers often face complex problems under uncertainty. Statistical and Machine Learning (ML) tools can support these decisions by reducing the lack of knowledge. However, in many real-world scenarios, the uncertainty itself is induced by the decisions taken. In such cases, standard ML models that provide a priori insights of the problem environment become ineffective. In the context of decision-dependent uncertainty, a promising approach is Constraint Learning (CL). According to this procedure, a pretrained ML model is embedded into the optimization model to capture relationships between uncertain parameters and decision variables that must be set in advance. However, the dependency between decision and response variables is often not known with certainty due to epistemic errors in the prediction model. To address this limitation within a robust optimization framework, we propose an extension of CL that constructs decision-dependent uncertainty sets using a Quantile Surface Neural Network (QSNN). The QSNN learns multi-dimensional conditional quantile functions from data, allowing the characterization of uncertainty that varies across the decision space. Since embedding neural networks within optimization problems introduces additional complexity, we propose an initial solution approach to handle this integration effectively. To demonstrate the practical relevance of our methodology, we apply it to an energy hub management problem. In this case study, the energy consumption of a group of users is partially sensitive to the day-ahead tariff set by the hub. Preliminary results highlight the potential of the proposed approach in managing demand-side uncertainty and improving operational efficiency.
