you can see it here as well now usually we have one policy and one reward right and so what we do is we improve the policy and that leads us to better evaluate the q function for a given reward function and that leads us to improve the policy now this paper is going to transform this into the following we have many policies so we have policy one policy two and so on until policy i don't know p and we also have many reward functions reward 1 reward 2 reward 3 and so on until reward let's call that r so we have