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Citing Wikipedia:

The goal in a Markov decision process is to find a good "policy" for the decision maker: a function $\pi$ that specifies the action $\pi(s)$ that the decision maker will choose when in state $s$. Once a Markov decision process is combined with a policy in this way, this fixes the action for each state and the resulting combination behaves like a Markov chain (since the action chosen in state $s$ is completely determined by $\pi(s)$ and $\Pr(s_{t+1}=s'\mid > s_{t}=s,a_{t}=a)$ $\Pr(s_{t+1}=s'\mid s_{t}=s,a_{t}=a)$ reduces to $Pr(s_{t+1}=s'\mid s_{t}=s)$ $Pr(s_{t+1}=s'\mid s_{t}=s)$, a Markov transition matrix).

A policy that maximizes the function above is called an optimal policy and is usually denoted $\pi^*$. A particular MDP may have multiple distinct optimal policies. Because of the Markov property, it can be shown that the optimal policy is a function of the current state, as assumed above.

Can the policy be considered a random variable?

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  • $\begingroup$ The answer is in the question: "the optimal policy is a function of the current state". $\endgroup$ – Xi'an Oct 2 '20 at 6:38
  • $\begingroup$ A function of a random variable is a random variable? $\endgroup$ – Julio Jesus Luna Oct 2 '20 at 14:25
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The policy is a function you define to act in an environment, it's not a random variable.

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