Q-learning can be difficult to use in continuous action spaces, because an optimization has to be solved to find the maximal action for the action-values. A common strategy has been to restrict the functional form of the action-values to be concave in the actions, to simplify the optimization. Such restrictions, however, can prevent learning accurate action-values. In this work, we propose a new policy search objective that facilitates using Q-learning and a framework to optimize this objective, called Actor-Expert. The Expert uses Q-learning to update the action-values towards optimal action-values. The Actor learns the maximal actions over time for these changing action-values. We develop a Cross Entropy Method (CEM) for the Actor, where such a global optimization approach facilitates use of generically parameterized action-values. This method - which we call Conditional CEM - iteratively concentrates density around maximal actions, conditioned on state. We prove that this algorithm tracks the expected CEM update, over states with changing action-values. We demonstrate in a toy environment that previous methods that restrict the action-value parameterization fail whereas Actor-Expert with a more general action-value parameterization succeeds. Finally, we demonstrate that Actor-Expert performs as well as or better than competitors on four benchmark continuous-action environments.
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