Learning All Optimal Policies with Multiple Criteria

We describe an algorithm for learning in the presence of multiple criteria. Our technique generalizes previous approaches in that it can learn optimal policies for any linear preference assignment over the multiple reward criteria. The algorithm can be viewed as an extension to standard reinforcement learning for MDPs where instead of repeatedly backing up maximal expected rewards, we back up the set of expected rewards that are maximal for some set of linear preferences (given by a weight vector, w). We present the algorithm, along with a proof of correctness showing that our solution gives the optimal policy for any linear preference function. The solution reduces to the standard value iteration algorithm for a specific weight vector.