A Markovian decision process
Open accessAbstract
The purpose of this paper is to discuss the asymptotic behavior of the sequence (f sub n(i)) generated by a nonlinear recurrence relation. This problem arises in connection with an equipment replacement problem, cf. S. Dreyfus, A Note on an Industrial Replacement Process.
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Deep reinforcement learning models are based on the Markov decision process and Q-learning adapted to neural networks.
“For example, deep reinforcement learning models (30, 31) are based on well-known concepts such as the Markov decision process (MDP) (32) and Q-learning (33) adapted to neural networks.”
From Accessing Artificial Intelligence for Clinical Decision-Making (2021) · cites this paper as [32]
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Cites
Bellman, R. (1956) · Canadian Journal of Mathematics · doi:10.4153/cjm-1956-023-8 · Cited by 22 · see citing works
Self-citationA Note on an Industrial Replacement Process
Dreyfus, S. E. (1957) · Journal of the Operational Research Society · doi:10.1057/jors.1957.30 · Cited by 16 · see citing works
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Research works printed but not linked: 2
- [2][2] —, Dynamic Programming, Princeton University Press, 1957. -
- [3][3] Functional equations in the theory of dynamic programming, II. Nonlinear differential equations, Proc. Nat. Acad. Sci. 41 (1955) pp. 482–5. -
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- Authors
- Bellman, R.
- Corresponding author
- Bellman, Richard
- Venue
- Indiana University Mathematics Journal
- Published
- 1957
- Volume
- 6
- Issue
- 4
- Pages
- 679-684
- ISSN
- 0022-2518 (ISSN-L)
- OpenAlex
- W2076337359
- Cited by
- 2,408
- References
- 2
- Citations by year
- 2026: 62 · 2025: 204 · 2024: 245 · 2023: 238 · 2022: 219 · 2021: 243 · 2020: 185 · 2019: 172 · 2018: 140 · 2017: 108 · 2016: 93 · 2015: 82 · 2014: 63 · 2013: 65 · 2012: 61
- FWCI
- 1.58
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Indiana University Mathematics Journal (publishedVersion)
- Defense Technical Information Center (DTIC) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Adaptive Dynamic Programming Control
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- nonlinear recurrence relations, asymptotic behavior, replacement policy
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