Risk-Sensitivity Vanishing Limit for Controlled Markov Processes

In this paper, we prove that the optimal risk-sensitive reward for Markov decision processes with compact state space and action space converges to the optimal average reward as the risk-sensitive factor tends to 0. In doing so, a variational formula for the optimal risk-sensitive reward is derived....

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Veröffentlicht in:Journal of dynamical and control systems 2023-10, Vol.29 (4), p.1471-1508
Hauptverfasser: Dai, Yanan, Chen, Jinwen
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we prove that the optimal risk-sensitive reward for Markov decision processes with compact state space and action space converges to the optimal average reward as the risk-sensitive factor tends to 0. In doing so, a variational formula for the optimal risk-sensitive reward is derived. An extension of the Kreĭn-Rutman Theorem to certain nonlinear operators is involved. Based on these, partially observable Markov decision processes are also investigated. A portfolio optimization problem is presented as an example of an application of the approach, in which a duality-relation between the maximization of risk-sensitive reward and the maximization of upside chance for out-performance over the optimal average reward is established.
ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-023-09641-5