Data-Driven DRO and Economic Decision Theory: An Analytical Synthesis With Bayesian Nonparametric Advancements
This work addresses the integration of optimization and economic theory for decision-making under uncertainty, which is incremental as it builds on existing DRO and DTA models.
The paper tackles the problem of bridging data-driven Distributionally Robust Optimization (DRO) and Economic Decision Theory under Ambiguity by developing a unified framework and a novel DRO approach using Bayesian nonparametric tools like Dirichlet Processes, with results showing favorable performance in prediction accuracy and stability through simulations and real-data experiments.
We develop an analytical synthesis that bridges data-driven Distributionally Robust Optimization (DRO) and Economic Decision Theory under Ambiguity (DTA). By reinterpreting standard regularization and DRO techniques as data-driven counterparts of ambiguity-averse decision models, we provide a unified framework that clarifies their intrinsic connections. Building on this synthesis, we propose a novel DRO approach that leverages a popular DTA model of smooth ambiguity-averse preferences together with tools from Bayesian nonparametric statistics. Our baseline framework employs Dirichlet Process (DP) posteriors, which naturally extend to heterogeneous data sources via Hierarchical Dirichlet Processes (HDPs), and can be further refined to induce outlier robustness through a procedure that selectively filters poorly-fitting observations during training. Theoretical performance guarantees and convergence results, together with extensive simulations and real-data experiments, illustrate the method's favorable performance in terms of prediction accuracy and stability.