Result of Reinforcement learning
Is the result of RL is a classic function to (re)apply at each time step?
In some manner yes, when using RL to find the best policy you end up with a policy that can be described as a function(classic or not) from possible states to possible actions.  

As if it was a regression?
No, regression algorithms 'solves' the function between feature space and target space.
 In RL both of these spaces have no(very different) meanings.
In addition, RL algorithms take into consideration multi-step predictions(state transitions + rewards), which is not very straight-forward in regression problems.