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


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
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.