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Conditions for optimality in dynamic programming and for the limit of \(n\)-stage optimal policies to be optimal. (English) Zbl 0316.90080


MSC:

90C40 Markov and semi-Markov decision processes
91A35 Decision theory for games
49L20 Dynamic programming in optimal control and differential games
93E20 Optimal stochastic control
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[1] Ash, R. B., Real Analysis and Probability (1972), New York: Academic Press, New York · Zbl 1381.28001
[2] Blackwell, D., Discounted dynamic programming, Ann. Math. Statist., 36, 226-235 (1965) · Zbl 0133.42805
[3] Blackwell, D., On stationary policies, J. Royal Statist. Soc., 133, 33-37 (1971)
[4] Dubins, L. E.; Savage, L. J., How to gamble if you must (1965), New York: McGraw-Hill, New York · Zbl 0133.41402
[5] Furukawa, N., Markovian decision processes with compact action spaces, Ann. Math. Statist., 43, 1612-1622 (1972) · Zbl 0277.90083
[6] Hinderer, K., Foundations of non-stationary dynamic programming with discrete time-parameter (1970), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0202.18401
[7] Hinderer, K., InstationÄre dynamische Optimierung bei schwachen Voraussetzungen über die Gewinnfunktionen, Abh. math. Sem. Univ. Hamburg, 36, 208-223 (1971) · Zbl 0246.49026
[8] Hordijk, A., Dynamic Programming and Markov Potential Theory (1974), Amsterdam: Mathematical Centre Tracts 51, Amsterdam
[9] Kuratowski, K., Topology I (1966), New York: Academic Press, New York
[10] Kuratowski, K., Topology II (1968), New York: Academic Press, New York
[11] Maitra, A., Discounted dynamic programming on compact metric spaces, Sankhya, 30, 211-216 (1968) · Zbl 0187.17702
[12] Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc., 71, 152-182 (1951) · Zbl 0043.37902
[13] Rieder, U.: Bayesian dynamic programming (To be published) · Zbl 0316.90081
[14] Rieder, U.: On stopped decision processes with discrete time parameter (To be published) · Zbl 0326.90065
[15] SchÄl, M.; Henn, R., Ein verallgemeinertes stationÄres Entscheidungsmodell der dynamischen Optimierung. Vol. X, Methods of operations research, 145-162 (1971), Meisenheim: Anton Hain, Meisenheim
[16] SchÄl, M., On continuous dynamic programming with discrete time-parameter, Z. Wahrscheinlichkeitstheorie verw. Geb., 21, 279-288 (1972) · Zbl 0213.45402
[17] SchÄl, M.: Dynamische Optimierung unter Stetigkeits- und Kompaktheitsbedingungen. Habilitationsschrift, Univ. Hamburg 1972
[18] SchÄl, M., A selection theorem for optimization problems, Arch. Math., XXV, 219-224 (1974) · Zbl 0351.90069
[19] SchÄl, M.: On dynamic programming: compactness of the space of policies (To appear in Stochastic Processes Appl. A summary of this paper may be found in [20]) · Zbl 0317.60025
[20] SchÄl, M., Dynamic programming under continuity and compactness assumptions, Advances Appl. Probability, 5, 28-29 (1973)
[21] Strauch, R. E., Negative dynamic programming, Ann. Math. Statist., 37, 871-890 (1966) · Zbl 0144.43201
[22] Sudderth, W. D., On the Dubins and Savage characterization of optimal strategies, Ann. Math. Statist., 43, 498-507 (1972) · Zbl 0239.62052
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