What is the relation between the compatibile features and the state features in Actor Critic Algorithm?
$\phi(s)$ is the representation of the state, and $\psi$ is the gradient (of the log) of the policy. Essentially, those two don't really have any connection, except for that the input to the policy is the state's representation. That is, the policy will compute the appropriate action distribution according by using its model (say a neural network) when applied on the representation of a state.