View in EDS HTML Full Text PDF Full Text

Preference ambiguity and robustness in multistage decision making.

Saved in:
Bibliographic Details
Title: Preference ambiguity and robustness in multistage decision making.
Authors: Liu, Jia1,2 (AUTHOR) jialiu@xjtu.edu.cn, Chen, Zhiping1,2 (AUTHOR) zchen@mail.xjtu.edu.cn, Xu, Huifu3 (AUTHOR) hfxu@se.cuhk.edu.hk
Source: Mathematical Programming. Nov2025, Vol. 214 Issue 1/2, p847-939. 93p.
Subjects: Utility functions, Robust optimization, Decision making, Dynamic programming, Expectation-maximization algorithms, Decomposition method
Abstract: In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical path and the information on the true utility function is incomplete. To mitigate the adverse impact arising from ambiguity regarding the true utility, we propose a maximin robust model where the optimal policy is based on the worst-case sequence of utility functions from an ambiguity set constructed with partially available information about the decision maker's preferences. We show that the multistage maximin problem is time consistent when the utility functions depend on the historical path and provide a counter example demonstrating that the time consistency is not retained when the utility functions are stagewise independent. With the time consistency, we show the maximin problem can be recursively solved by backward induction, where a one-stage maximin problem is solved at each stage starting from the last stage. Moreover, we propose two approaches to construct the ambiguity set: a pairwise comparison approach and a ζ -ball approach where a ball of utility functions centered at a nominal utility function under ζ -metric is considered. To overcome the difficulty arising from solving the infinite-dimensional optimization problem in the computation of the worst-case expected utility value, we propose a piecewise linear approximation of the utility functions and derive error bounds for the approximation under moderate conditions. Finally, we use the stochastic dual dynamic programming method and the nested Benders' decomposition method to solve the multistage historical-path-dependent preference robust problem and the scenario tree method to solve the stagewise-independent problem. We carry out comparative analysis on the efficiency of the computational schemes as well as out-of-sample performances of the historical-path-dependent and stagewise-independent models. The preliminary results show that the historical-path-dependent preference robust model displays overall superiority. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Programming is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 189704712
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Preference ambiguity and robustness in multistage decision making.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Jia%22">Liu, Jia</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> jialiu@xjtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Chen%2C+Zhiping%22">Chen, Zhiping</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zchen@mail.xjtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Xu%2C+Huifu%22">Xu, Huifu</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> hfxu@se.cuhk.edu.hk</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Mathematical+Programming%22">Mathematical Programming</searchLink>. Nov2025, Vol. 214 Issue 1/2, p847-939. 93p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Utility+functions%22">Utility functions</searchLink><br /><searchLink fieldCode="DE" term="%22Robust+optimization%22">Robust optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Decision+making%22">Decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+programming%22">Dynamic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Expectation-maximization+algorithms%22">Expectation-maximization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Decomposition+method%22">Decomposition method</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we consider a multistage expected utility maximization problem where the decision maker's utility function at each stage depends on historical path and the information on the true utility function is incomplete. To mitigate the adverse impact arising from ambiguity regarding the true utility, we propose a maximin robust model where the optimal policy is based on the worst-case sequence of utility functions from an ambiguity set constructed with partially available information about the decision maker's preferences. We show that the multistage maximin problem is time consistent when the utility functions depend on the historical path and provide a counter example demonstrating that the time consistency is not retained when the utility functions are stagewise independent. With the time consistency, we show the maximin problem can be recursively solved by backward induction, where a one-stage maximin problem is solved at each stage starting from the last stage. Moreover, we propose two approaches to construct the ambiguity set: a pairwise comparison approach and a ζ -ball approach where a ball of utility functions centered at a nominal utility function under ζ -metric is considered. To overcome the difficulty arising from solving the infinite-dimensional optimization problem in the computation of the worst-case expected utility value, we propose a piecewise linear approximation of the utility functions and derive error bounds for the approximation under moderate conditions. Finally, we use the stochastic dual dynamic programming method and the nested Benders' decomposition method to solve the multistage historical-path-dependent preference robust problem and the scenario tree method to solve the stagewise-independent problem. We carry out comparative analysis on the efficiency of the computational schemes as well as out-of-sample performances of the historical-path-dependent and stagewise-independent models. The preliminary results show that the historical-path-dependent preference robust model displays overall superiority. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Mathematical Programming is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=189704712
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10107-025-02208-1
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 93
        StartPage: 847
    Subjects:
      – SubjectFull: Utility functions
        Type: general
      – SubjectFull: Robust optimization
        Type: general
      – SubjectFull: Decision making
        Type: general
      – SubjectFull: Dynamic programming
        Type: general
      – SubjectFull: Expectation-maximization algorithms
        Type: general
      – SubjectFull: Decomposition method
        Type: general
    Titles:
      – TitleFull: Preference ambiguity and robustness in multistage decision making.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Liu, Jia
      – PersonEntity:
          Name:
            NameFull: Chen, Zhiping
      – PersonEntity:
          Name:
            NameFull: Xu, Huifu
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 00255610
          Numbering:
            – Type: volume
              Value: 214
            – Type: issue
              Value: 1/2
          Titles:
            – TitleFull: Mathematical Programming
              Type: main
ResultId 1