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Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs

Beatris A. Escobedo-Trujillo; Carmen G. Higuera-Chan — 2019

Kybernetika

In this paper we are concerned with a class of time-varying discounted Markov decision models $ℳ_{n}$ with unbounded costs $c_{n}$ and state-action dependent discount factors. Specifically we study controlled systems whose state process evolves according to the equation $x_{n + 1} = G_{n} (x_{n}, a_{n}, ξ_{n}), n = 0, 1, ...$ , with state-action dependent discount factors of the form $α_{n} (x_{n}, a_{n})$ , where $a_{n}$ and $ξ_{n}$ are the control and the random disturbance at time $n$ , respectively. Assuming that the sequences of functions ${α_{n}}$ , ${c_{n}}$ and ${G_{n}}$ converge, in certain sense, to $α_{\infty}$ , $c_{\infty}$ and $G_{\infty}$ , our...

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