Work

An axiomatic analysis of distributionally robust optimization with q-norm ambiguity sets for probability smoothing

Year: 2026

Type: article

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 ∈ [1, ∞], the q -DRO estimator satisfies the fundamental axioms of Positivity and Symmetry. For the case of q ∈ (1, ∞), 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.

Source: Operations Research Letters

DOI: 10.1016/j.orl.2026.107457

Authors: Yoichi Izunaga, Kota Kurihara, Hokuto Nagano, Daiki Uchida

Institution: Kyushu University

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,960

Funder: Japan Society for the Promotion of Science