Data-Driven DRO and Economic Decision Theory: An Analytical Synthesis With Bayesian Nonparametric Advancements

TL;DR

This paper unifies data-driven DRO and economic decision theory under ambiguity, introducing a Bayesian nonparametric approach with Dirichlet Processes for robust, accurate decision-making across heterogeneous data sources.

Contribution

It provides a novel synthesis linking DRO and DTA, and develops a Bayesian nonparametric DRO method with theoretical guarantees and outlier robustness.

Findings

Enhanced prediction accuracy and stability in experiments

Effective outlier filtering during training

Theoretical guarantees on convergence and performance

Abstract

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.