On the coefficients of prescriptiveness in contextual optimization

Bo Jiang; Xuecheng Tian; Shuaian Wang; Bo Jiang; Xuecheng Tian; Shuaian Wang

doi:10.3934/era.2026266

Electronic Research Archive

2026, Volume 34, Issue 9: 6011-6042. doi: 10.3934/era.2026266

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On the coefficients of prescriptiveness in contextual optimization

Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China

Received: 22 April 2026 Revised: 10 June 2026 Accepted: 24 June 2026 Published: 13 July 2026

This paper focused on the coefficients of prescriptiveness in the field of contextual optimization, which measure the efficacy of a prescriptive analytics method in leveraging contextual information for prescribing data-driven decisions. We identified two key deficiencies of the original coefficient of prescriptiveness proposed in the literature. First, this coefficient is problem-dependent, i.e., it lacks a universal scale: its asymptotic upper bound (less than or equal to 1) varies across problems, making cross-problem comparisons infeasible. Second, this coefficient is data-dependent, i.e., its calculation is contingent on specific training and test datasets, limiting its generalizability. To address the two deficiencies, we proposed two novel coefficients of prescriptiveness in this paper: (ⅰ) the adjusted coefficient of prescriptiveness, which replaces the deterministic perfect-foresight benchmark in the original coefficient with the full-information optimum; and (ⅱ) the expected coefficient of prescriptiveness, derived by taking the expectation over the sampling distribution of the training dataset. Meanwhile, we developed their empirical estimators for practical applications. Moreover, rigorous theoretical analysis established two fundamental properties of these coefficients of prescriptiveness. Through extensive numerical experiments based on the newsvendor problem, we validated the effectiveness of our proposed coefficients of prescriptiveness in addressing the identified deficiencies. By refining the evaluation framework for prescriptive analytics, this work advances the generalizability and applicability of the coefficients of prescriptiveness.
- prescriptive analytics,
- contextual optimization,
- coefficient of prescriptiveness,
- decision analysis
Citation: Bo Jiang, Xuecheng Tian, Shuaian Wang. On the coefficients of prescriptiveness in contextual optimization[J]. Electronic Research Archive, 2026, 34(9): 6011-6042. doi: 10.3934/era.2026266

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Abstract

This paper focused on the coefficients of prescriptiveness in the field of contextual optimization, which measure the efficacy of a prescriptive analytics method in leveraging contextual information for prescribing data-driven decisions. We identified two key deficiencies of the original coefficient of prescriptiveness proposed in the literature. First, this coefficient is problem-dependent, i.e., it lacks a universal scale: its asymptotic upper bound (less than or equal to 1) varies across problems, making cross-problem comparisons infeasible. Second, this coefficient is data-dependent, i.e., its calculation is contingent on specific training and test datasets, limiting its generalizability. To address the two deficiencies, we proposed two novel coefficients of prescriptiveness in this paper: (ⅰ) the adjusted coefficient of prescriptiveness, which replaces the deterministic perfect-foresight benchmark in the original coefficient with the full-information optimum; and (ⅱ) the expected coefficient of prescriptiveness, derived by taking the expectation over the sampling distribution of the training dataset. Meanwhile, we developed their empirical estimators for practical applications. Moreover, rigorous theoretical analysis established two fundamental properties of these coefficients of prescriptiveness. Through extensive numerical experiments based on the newsvendor problem, we validated the effectiveness of our proposed coefficients of prescriptiveness in addressing the identified deficiencies. By refining the evaluation framework for prescriptive analytics, this work advances the generalizability and applicability of the coefficients of prescriptiveness.

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