  Many policy gradient methods are variants of Actor-Critic (AC), where a value
function (critic) is learned to facilitate updating the parameterized policy
(actor). The update to the actor involves a log-likelihood update weighted by
the action-values, with the addition of entropy regularization for soft
variants. In this work, we explore an alternative update for the actor, based
on an extension of the cross entropy method (CEM) to condition on inputs
(states). The idea is to start with a broader policy and slowly concentrate
around maximal actions, using a maximum likelihood update towards actions in
the top percentile per state. The speed of this concentration is controlled by
a proposal policy, that concentrates at a slower rate than the actor. We first
provide a policy improvement result in an idealized setting, and then prove
that our conditional CEM (CCEM) strategy tracks a CEM update per state, even
with changing action-values. We empirically show that our Greedy AC algorithm,
that uses CCEM for the actor update, performs better than Soft Actor-Critic and
is much less sensitive to entropy-regularization.
