On uniformly nearly optimal stationary strategies

J. Wal, van der

Research output: Book/ReportReportAcademic

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Abstract

For Markov decision processes with countable state space and nonnegative immediate rewards Ornstein proved the existence of a stationary strategy f which is uniformly nearly optimal in the following multiplicative sense v(f) = (1 - e) v* . Strauch proved that if the immediate rewards are nonpositive and the action space is finite then a uniformly optimal stationary strategy exists. This paper connects these partial results and proves the following theorem for Markov decision processes with countable state space and arbitrary action space: if in each state where the value is nonpositive a conserving action exists then there is a stationary strategy f satisfying v(f) = V* - eu* where u* is the value of the problem if only the positive rewards are counted.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Hogeschool Eindhoven
Number of pages21
Publication statusPublished - 1981

Publication series

NameMemorandum COSOR
Volume8111
ISSN (Print)0926-4493

Fingerprint

Reward
Markov Decision Process
Countable
State Space
Multiplicative
Non-negative
Partial
Arbitrary
Theorem
Strategy

Cite this

Wal, van der, J. (1981). On uniformly nearly optimal stationary strategies. (Memorandum COSOR; Vol. 8111). Eindhoven: Technische Hogeschool Eindhoven.
Wal, van der, J. / On uniformly nearly optimal stationary strategies. Eindhoven : Technische Hogeschool Eindhoven, 1981. 21 p. (Memorandum COSOR).
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Wal, van der, J 1981, On uniformly nearly optimal stationary strategies. Memorandum COSOR, vol. 8111, Technische Hogeschool Eindhoven, Eindhoven.

On uniformly nearly optimal stationary strategies. / Wal, van der, J.

Eindhoven : Technische Hogeschool Eindhoven, 1981. 21 p. (Memorandum COSOR; Vol. 8111).

Research output: Book/ReportReportAcademic

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N2 - For Markov decision processes with countable state space and nonnegative immediate rewards Ornstein proved the existence of a stationary strategy f which is uniformly nearly optimal in the following multiplicative sense v(f) = (1 - e) v* . Strauch proved that if the immediate rewards are nonpositive and the action space is finite then a uniformly optimal stationary strategy exists. This paper connects these partial results and proves the following theorem for Markov decision processes with countable state space and arbitrary action space: if in each state where the value is nonpositive a conserving action exists then there is a stationary strategy f satisfying v(f) = V* - eu* where u* is the value of the problem if only the positive rewards are counted.

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Wal, van der J. On uniformly nearly optimal stationary strategies. Eindhoven: Technische Hogeschool Eindhoven, 1981. 21 p. (Memorandum COSOR).