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Samenvatting

(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.

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 blz. (Memorandum COSOR).

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title = "On stationary strategies",

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.",

author = "{Wal, van der}, J.",

year = "1981",

language = "English",

series = "Memorandum COSOR",

publisher = "Technische Hogeschool Eindhoven",

}

Wal, van der, J 1981, On stationary strategies. Memorandum COSOR, vol. 8114, Technische Hogeschool Eindhoven, Eindhoven.

Onderzoeksoutput: Boek/rapport › Rapport › Academic

TY - BOOK

T1 - On stationary strategies

AU - Wal, van der, J.

PY - 1981

Y1 - 1981

N2 - (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.

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.

M3 - Report

T3 - Memorandum COSOR

BT - On stationary strategies

PB - Technische Hogeschool Eindhoven

CY - Eindhoven

ER -

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