Academic Journal
On Average Optimality for Non-Stationary Markov Decision Processes in Borel Spaces.
| Title: | On Average Optimality for Non-Stationary Markov Decision Processes in Borel Spaces. |
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| Authors: | Guo, Xin1 (AUTHOR) guox87@mail.sysu.edu.cn, Huang, Yonghui2 (AUTHOR) hyongh5@mail.sysu.edu.cn, Zhang, Yi3 (AUTHOR) y.zhang.29@bham.ac.uk |
| Source: | Mathematics of Operations Research (INFORMS). Nov2025, Vol. 50 Issue 4, p2552-2576. 25p. |
| Subject Terms: | *Markov processes, *Decision making, *Algorithms, Borel sets, Time-varying systems, Existence theorems |
| Abstract: | This paper studies Borel models of nonstationary Markov decision processes (MDPs) with average criteria. We establish a suitable fixed point theorem, which is used to show the existence of solutions to the average optimality equation (AOE), without using contractions. The existence of optimal policies follows from the obtained solutions to the AOE. Furthermore, we show that versions of the rolling horizon algorithm can be used to produce an optimal policy or an ϵ-optimal policy. Finally, we compare the optimality conditions imposed in this paper with the existing ones in the literature, and demonstrate that they can be satisfied while the previous ones are not. Funding: This research was supported by National Key Research and Development Program of China [2022YFA1004600], National Natural Science Foundation of China [No. 12301170], Guangdong Basic and Applied Research Foundation [2023A1515012644], and the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University [No. 23qnpy39]. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences 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.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: On Average Optimality for Non-Stationary Markov Decision Processes in Borel Spaces. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Guo%2C+Xin%22">Guo, Xin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> guox87@mail.sysu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Yonghui%22">Huang, Yonghui</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hyongh5@mail.sysu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Yi%22">Zhang, Yi</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> y.zhang.29@bham.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Operations+Research+%28INFORMS%29%22">Mathematics of Operations Research (INFORMS)</searchLink>. Nov2025, Vol. 50 Issue 4, p2552-2576. 25p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br />*<searchLink fieldCode="DE" term="%22Decision+making%22">Decision making</searchLink><br />*<searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Borel+sets%22">Borel sets</searchLink><br /><searchLink fieldCode="DE" term="%22Time-varying+systems%22">Time-varying systems</searchLink><br /><searchLink fieldCode="DE" term="%22Existence+theorems%22">Existence theorems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper studies Borel models of nonstationary Markov decision processes (MDPs) with average criteria. We establish a suitable fixed point theorem, which is used to show the existence of solutions to the average optimality equation (AOE), without using contractions. The existence of optimal policies follows from the obtained solutions to the AOE. Furthermore, we show that versions of the rolling horizon algorithm can be used to produce an optimal policy or an ϵ-optimal policy. Finally, we compare the optimality conditions imposed in this paper with the existing ones in the literature, and demonstrate that they can be satisfied while the previous ones are not. Funding: This research was supported by National Key Research and Development Program of China [2022YFA1004600], National Natural Science Foundation of China [No. 12301170], Guangdong Basic and Applied Research Foundation [2023A1515012644], and the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University [No. 23qnpy39]. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/moor.2023.0169 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 2552 Subjects: – SubjectFull: Markov processes Type: general – SubjectFull: Decision making Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Borel sets Type: general – SubjectFull: Time-varying systems Type: general – SubjectFull: Existence theorems Type: general Titles: – TitleFull: On Average Optimality for Non-Stationary Markov Decision Processes in Borel Spaces. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Guo, Xin – PersonEntity: Name: NameFull: Huang, Yonghui – PersonEntity: Name: NameFull: Zhang, Yi IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 0364765X Numbering: – Type: volume Value: 50 – Type: issue Value: 4 Titles: – TitleFull: Mathematics of Operations Research (INFORMS) Type: main |
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