Finite state approximations for denumerable state infinite horizon discounted Markov decision processes with unbounded rewards
In very many Markov decision problems with denumerable states, the reward vector is unbounded. This paper deals with the approach to unbounded problems of \textit{J. M. Harrison} [Ann. Math. Staist. 43, 636-644 (1972; Zbl 0262.90064)], \textit{J. Wessels} [J. Math. Anal. Appl. 58, 326-335 (1977; Zbl 0354.90087)] and \textit{S. A. Lippman} [Manage. Sci., Theory 21, 1225-1233 (1975; Zbl 0309.90017)]. The approach is to use the results of these authors to convert the unbounded problems to bounded problems for which results in our earlier papers [e.g., J. Math. Anal. Appl. 74, 292- 295 (1980; Zbl 0428.90082); ibid. 72, 512-523 (1979; Zbl 0431.90080)] will then apply. The approximation errors are dependent on the appropriate contraction ratio factor for each case considered.
scientific article; zbMATH DE number 3847252