2025/07/21 by Radek Salač, Salač, Radek, Michael Kupper +3 · 1 voice
Business, Management and Accounting · Computer Science · Mathematics · #Big Data and Business Intelligence #Consistency (knowledge bases) #Exponential function #Function (biology) #Laplace transform #Large deviations theory #Neural Networks and Applications #Newsvendor model #Optimization problem #Regret #Stochastic optimization #math.OC #math.PR
paper · pdf · doi:10.48550/arxiv.2507.15215
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/07/21 · arxiv published 2025/07/21 · arxiv updated 2025/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data originating from heterogeneous sources or from randomly evolving data-generating mechanisms. We propose a decision-making approach that identifies optimal decisions for which a specific notion of risk of shifted regret decays to zero at a prescribed exponential rate. This optimal decision arises as the solution to a multi-objective optimization problem, which reflects asymptotic behavior properties of the data-generating process. Central to our framework is a rate function that characterizes this behavior via a Laplace principle, thereby generalizing standard concepts from large deviation theory. Our general formulation enables our approach to account for data from uncertain distributions and recovers classical results in data-driven decision making under uncertainty as special cases, including distributionally robust optimization. Moreover, our method enables decision-makers to systematically balance a desired rate of asymptotic risk decay against a potential loss in statistical consistency of the resulting data-driven decision. We demonstrate the effectiveness of the proposed approach through illustrative examples from operations research, such as the newsvendor problem, under aleatoric uncertainty induced by heterogeneous data sources.