  In Reinforcement Learning, the optimal action at a given state is dependent
on policy decisions at subsequent states. As a consequence, the learning
targets evolve with time and the policy optimization process must be efficient
at unlearning what it previously learnt. In this paper, we discover that the
policy gradient theorem prescribes policy updates that are slow to unlearn
because of their structural symmetry with respect to the value target. To
increase the unlearning speed, we study a novel policy update: the gradient of
the cross-entropy loss with respect to the action maximizing $q$, but find that
such updates may lead to a decrease in value. Consequently, we introduce a
modified policy update devoid of that flaw, and prove its guarantees of
convergence to global optimality in $\mathcal{O}(t^{-1})$ under classic
assumptions. Further, we assess standard policy updates and our cross-entropy
policy updates along six analytical dimensions. Finally, we empirically
validate our theoretical findings.
