{"ID":2892039,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15215","arxiv_id":"2507.15215","title":"Asymptotic Optimality in Data-Driven Decision Making","abstract":"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.","short_abstract":"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 mechanis...","url_abs":"https://arxiv.org/abs/2507.15215","url_pdf":"https://arxiv.org/pdf/2507.15215v2","authors":"[\"Radek Salač\",\"Michael Kupper\",\"Tobias Sutter\"]","published":"2025-07-21T03:30:12Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}