{"ID":2837365,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.18815","arxiv_id":"2511.18815","title":"An Axiomatic Analysis of Distributionally Robust Optimization with $q$-Norm Ambiguity Sets for Probability Smoothing","abstract":"We analyze the axiomatic properties of a class of probability estimators derived from Distributionally Robust Optimization (DRO) with $q$-norm ambiguity sets ($q$-DRO), a principled approach to the zero-frequency problem. While classical estimators such as Laplace smoothing are characterized by strong linearity axioms like Ratio Preservation, we show that $q$-DRO provides a flexible alternative that satisfies other desirable properties. We first prove that for any $q \\in [1, \\infty]$, the $q$-DRO estimator satisfies the fundamental axioms of Positivity and Symmetry. For the case of $q \\in (1, \\infty)$, we then prove that it also satisfies Order Preservation. Our analysis of the optimality conditions also reveals that the $q$-DRO formulation is equivalent to the regularized empirical loss minimization.","short_abstract":"We analyze the axiomatic properties of a class of probability estimators derived from Distributionally Robust Optimization (DRO) with $q$-norm ambiguity sets ($q$-DRO), a principled approach to the zero-frequency problem. While classical estimators such as Laplace smoothing are characterized by strong linearity axioms...","url_abs":"https://arxiv.org/abs/2511.18815","url_pdf":"https://arxiv.org/pdf/2511.18815v6","authors":"[\"Yoichi Izunaga\",\"Kota Kurihara\",\"Hokuto Nagano\",\"Daiki Uchida\"]","published":"2025-11-24T06:49:42Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}