Abstract
Firstly we introduce MDPs with finite state spaces, prove the reward iteration and derive the basic solution techniques: value iteration and optimality criterion. Then MDPs with finite transition law are considered. There the set of reachable states is finite.
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References
Almudevar, A. (2014). Approximate iterative algorithms. Leiden: CRC Press/Balkema.
Bellman, R. (1957). Dynamic programming. Princeton: Princeton University Press.
Berry, D. A., & Fristedt, B. (1985). Bandit problems. London: Chapman & Hall.
Bertsekas, D. P. (1976). Dynamic programming and stochastic control. New York: Academic Press.
Bertsekas, D. P. (1995). Dynamic programming and optimal control. Belmont: Athena Scientific.
Bertsekas, D. P., & Shreve, S. E. (1978). Stochastic optimal control. New York: Academic Press.
Blackwell, D. (1962). Discrete dynamic programming. The Annals of Mathematical Statistics, 33, 719–726.
Blackwell, D. (1965). Discounted dynamic programming. The Annals of Mathematical Statistics, 36, 226–235.
Chang, H. S., Fu, M. C., Hu, J., & Marcus, S. I. (2007). Simulation-based algorithms for Markov decision processes. London: Springer.
Dvoretzky, A., Kiefer, J., & Wolfowitz, J. (1952a). The inventory problem. I. Case of known distributions of demand. Econometrica, 20, 187–222.
Dvoretzky, A., Kiefer, J., & Wolfowitz, J. (1952b). The inventory problem. II. Case of unknown distributions of demand. Econometrica, 20, 450–466.
Dynkin, E. B. (1965). Markov processes (Vols. I, II). New York: Academic Press.
Dynkin, E. B., & Yushkevich, A. A. (1979). Controlled Markov processes. Berlin: Springer.
Hernández-Lerma, O. (1989). Adaptive Markov control processes. New York: Springer.
Heyman, D., & Sobel, M. (1984). Stochastic models in operations research: Stochastic optimization. New York: McGraw-Hill.
Hinderer, K. (1970). Foundations of non-stationary dynamic programming with discrete time parameter (Lecture Notes in Operations Research and Mathematical Systems, Vol. 33). Berlin: Springer.
Hinderer, K. (1976). Estimates for finite-stage dynamic programs. Journal of Mathematical Analysis and Applications, 55, 207–238.
Hinderer, K., & Hübner, G. (1977). An improvement of J. F. Shapiro’s turnpike theorem for the horizon of finite stage discrete dynamic programs. In Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Vol. A, pp. 245–255). Dordrecht: Reidel.
Hordijk, A. (1974). Dynamic programming and Markov potential theory. Amsterdam: Mathematisch Centrum.
Howard, G. T., & Nemhauser, G. L. (1968). Optimal capacity expansion. Naval Research Logistics Quarterly, 15, 535–550.
Howard, R. A. (1960). Dynamic programming and Markov processes. Cambridge: Technology Press of Massachusetts Institute of Technology.
Hübner, G. (1980). Bounds and good policies in stationary finite-stage Markovian decision problems. Advances in Applied Probability, 12, 154–173.
Karlin, S. (1955). The structure of dynamic programming models. Naval Research Logistics Quarterly, 2, 285–294 (1956).
Powell, W. B. (2007). Approximate dynamic programming. New York: Wiley.
Puterman, M. L. (1994). Markov decision processes: Discrete stochastic dynamic programming. New York: Wiley.
Ross, S. M. (1970). Applied probability models with optimization applications. San Francisco: Holden-Day.
Ross, S. M. (1983). Introduction to stochastic dynamic programming (Probability and Mathematical Statistics). New York: Academic Press.
Whittle, P. (1982). Optimization over time (Vol. I). Chichester: Wiley.
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Hinderer, K., Rieder, U., Stieglitz, M. (2016). Markovian Decision Processes with Finite Transition Law. In: Dynamic Optimization. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-48814-1_12
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