Optimal Stopping of Markov Chain and Three Abstract Optimization Problems
نویسنده
چکیده
There is a well known connection between three problems related to Optimal Stopping of Markov Chain and the equality of three corresponding indices: the classical Gittins index in the Ratio Maximization Problem, the Kathehakis-Veinot index in a Restart Problem, and Whittle index in a family of Retirement Problems. In [13] these three problems and these three indices were generalized in such a way that it become possible to use the State Elimination algorithm [11] to calculate this common Generalized Gittins index α. The main goal of this note is to demonstrate that the equality of these (generalized) indices is a special case of a more general relation between three simple abstract optimization problems.optimization problems.
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