On stationary strategies

J. Wal, van der

Research output: Book/ReportReportAcademic

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Abstract

(Extended version of Memorandum COSOR 81-11) This paper deals with total reward Markov decision processes with countable state space and extends various results on (nearly-)optimal stationary strategies. Strauch proved that if the rewards are nonpositive and the action space is finite then an optimal stationary strategy exists. For the case of nonnegative rewards Ornstein proved the existence of a stationary strategy f which is uniformly nearly-optimal in the multiplicative sense: v(f) = (1 - e) v* . Van der Wal showed that if the action space is finite then for each initial state a stationary nearly-optimal strategy exists. These partial results are connected and extended in the following theorem. If in each state where the value is nonpositive a conserving action exists then there exists a stationary strategy f which is uniformly nearly optimal in the following sense: v(f) = v* - eu* , where u * is the value of the problem if only the positive rewards are counted. Further the following result is established: if an optimal strategy exists then also an optimal stationary.strategy exists. This generalizes results of Strauch and Ornstein for the negative and positive dynamic programming cases respectively.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Hogeschool Eindhoven
Number of pages23
Publication statusPublished - 1981

Publication series

NameMemorandum COSOR
Volume8114
ISSN (Print)0926-4493

Fingerprint

Reward
Optimal Strategy
Markov Decision Process
Dynamic Programming
Countable
Strategy
Multiplicative
State Space
Non-negative
Partial
Generalise
Theorem

Cite this

Wal, van der, J. (1981). On stationary strategies. (Memorandum COSOR; Vol. 8114). Eindhoven: Technische Hogeschool Eindhoven.
Wal, van der, J. / On stationary strategies. Eindhoven : Technische Hogeschool Eindhoven, 1981. 23 p. (Memorandum COSOR).
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Wal, van der, J 1981, On stationary strategies. Memorandum COSOR, vol. 8114, Technische Hogeschool Eindhoven, Eindhoven.

On stationary strategies. / Wal, van der, J.

Eindhoven : Technische Hogeschool Eindhoven, 1981. 23 p. (Memorandum COSOR; Vol. 8114).

Research output: Book/ReportReportAcademic

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AB - (Extended version of Memorandum COSOR 81-11) This paper deals with total reward Markov decision processes with countable state space and extends various results on (nearly-)optimal stationary strategies. Strauch proved that if the rewards are nonpositive and the action space is finite then an optimal stationary strategy exists. For the case of nonnegative rewards Ornstein proved the existence of a stationary strategy f which is uniformly nearly-optimal in the multiplicative sense: v(f) = (1 - e) v* . Van der Wal showed that if the action space is finite then for each initial state a stationary nearly-optimal strategy exists. These partial results are connected and extended in the following theorem. If in each state where the value is nonpositive a conserving action exists then there exists a stationary strategy f which is uniformly nearly optimal in the following sense: v(f) = v* - eu* , where u * is the value of the problem if only the positive rewards are counted. Further the following result is established: if an optimal strategy exists then also an optimal stationary.strategy exists. This generalizes results of Strauch and Ornstein for the negative and positive dynamic programming cases respectively.

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Wal, van der J. On stationary strategies. Eindhoven: Technische Hogeschool Eindhoven, 1981. 23 p. (Memorandum COSOR).