Expected Long Term Cost for a Policy in an MDP

Topics: Policy Improvement Method for MDPs - Markov Decision Process

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(theorem)

In the context of an MDP, the expected long term cost for a given policy $r$ can be expressed as:

$$g\{r\}=\sum _{i=0}^m{\pi }_i{C}_{ik}$$

…where ${\pi }_i$ denotes the steady state probability of the state $i$.

Do not forget that the policy $r$ defines which decision $k$ is made in which state $i$.