  In this work we continue to build upon recent advances in reinforcement
learning for finite Markov processes. A common approach among previous existing
algorithms, both single-actor and distributed, is to either clip rewards or to
apply a transformation method on Q-functions to handle a large variety of
magnitudes in real discounted returns. We theoretically show that one of the
most successful methods may not yield an optimal policy if we have a
non-deterministic process. As a solution, we argue that distributional
reinforcement learning lends itself to remedy this situation completely. By the
introduction of a conjugated distributional operator we may handle a large
class of transformations for real returns with guaranteed theoretical
convergence. We propose an approximating single-actor algorithm based on this
operator that trains agents directly on unaltered rewards using a proper
distributional metric given by the Cram\'er distance. To evaluate its
performance in a stochastic setting we train agents on a suite of 55 Atari 2600
games using sticky-actions and obtain state-of-the-art performance compared to
other well-known algorithms in the Dopamine framework.
