Zero-Sum Games for piecewise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916244304691200 |
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| author | Golui, Subrata |
| author_facet | Golui, Subrata |
| contents | This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates are allowed to be un-unbounded from below and above. Under some mild conditions, we show the existence of the value of the game and an optimal randomized Markov saddle-point equilibrium in the class of all admissible feedback strategies. By studying the corresponding risk-sensitive finite-horizon optimal differential equations out of a class of possibly unbounded functions, to which the extended Feynman-Kac formula is also justified to hold, we obtain our required results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-Sum Games for piecewise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion Golui, Subrata Optimization and Control Probability This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates are allowed to be un-unbounded from below and above. Under some mild conditions, we show the existence of the value of the game and an optimal randomized Markov saddle-point equilibrium in the class of all admissible feedback strategies. By studying the corresponding risk-sensitive finite-horizon optimal differential equations out of a class of possibly unbounded functions, to which the extended Feynman-Kac formula is also justified to hold, we obtain our required results. |
| title | Zero-Sum Games for piecewise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2405.08012 |