Nonatomic total rewards Markov decision processes with multiple criteria |
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Authors: | Eugene A Feinberg Aleksey B Piunovskiy |
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Institution: | a Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA b Department of Mathematical Sciences, The University of Liverpool, M & O Building, Liverpool, L69 7ZL, UK |
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Abstract: | We consider a Markov decision process with an uncountable state space for which the vector performance functional has the form of expected total rewards. Under the single condition that initial distribution and transition probabilities are nonatomic, we prove that the performance space coincides with that generated by nonrandomized Markov policies. We also provide conditions for the existence of optimal policies when the goal is to maximize one component of the performance vector subject to inequality constraints on other components. We illustrate our results with examples of production and financial problems. |
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