A deficiency of prescriptive analytics—No perfect predicted value or predicted distribution exists

Shuaian Wang; Xuecheng Tian; Ran Yan; Yannick Liu; Shuaian Wang; Xuecheng Tian; Ran Yan; Yannick Liu

doi:10.3934/era.2022183

Electronic Research Archive

2022, Volume 30, Issue 10: 3586-3594. doi: 10.3934/era.2022183

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A deficiency of prescriptive analytics—No perfect predicted value or predicted distribution exists

1.
Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
2.
Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: 26 June 2022 Revised: 08 July 2022 Accepted: 18 July 2022 Published: 28 July 2022

Researchers and industrial practitioners are now interested in combining machine learning (ML) and operations research and management science to develop prescriptive analytics frameworks. By and large, a single value or a discrete distribution with a finite number of scenarios is predicted using an ML model with an unknown parameter; the value or distribution is then fed into an optimization model with the unknown parameter to prescribe an optimal decision. In this paper, we prove a deficiency of prescriptive analytics, i.e., that no perfect predicted value or perfect predicted distribution exists in some cases. To illustrate this phenomenon, we consider three different frameworks of prescriptive analytics, namely, the predict-then-optimize framework, smart predict-then-optimize framework and weighted sample average approximation (w-SAA) framework. For these three frameworks, we use examples to show that prescriptive analytics may not be able to prescribe a full-information optimal decision, i.e., the optimal decision under the assumption that the distribution of the unknown parameter is given. Based on this finding, for practical prescriptive analytics problems, we suggest comparing the prescribed results among different frameworks to determine the most appropriate one.
- prescriptive analytics,
- predict-then-optimize,
- smart predict-then-optimize,
- weighted sample average approximation
Citation: Shuaian Wang, Xuecheng Tian, Ran Yan, Yannick Liu. A deficiency of prescriptive analytics—No perfect predicted value or predicted distribution exists[J]. Electronic Research Archive, 2022, 30(10): 3586-3594. doi: 10.3934/era.2022183

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Abstract

Researchers and industrial practitioners are now interested in combining machine learning (ML) and operations research and management science to develop prescriptive analytics frameworks. By and large, a single value or a discrete distribution with a finite number of scenarios is predicted using an ML model with an unknown parameter; the value or distribution is then fed into an optimization model with the unknown parameter to prescribe an optimal decision. In this paper, we prove a deficiency of prescriptive analytics, i.e., that no perfect predicted value or perfect predicted distribution exists in some cases. To illustrate this phenomenon, we consider three different frameworks of prescriptive analytics, namely, the predict-then-optimize framework, smart predict-then-optimize framework and weighted sample average approximation (w-SAA) framework. For these three frameworks, we use examples to show that prescriptive analytics may not be able to prescribe a full-information optimal decision, i.e., the optimal decision under the assumption that the distribution of the unknown parameter is given. Based on this finding, for practical prescriptive analytics problems, we suggest comparing the prescribed results among different frameworks to determine the most appropriate one.

References

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