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?
