  We present the first class of policy-gradient algorithms that work with both
state-value and policy function-approximation, and are guaranteed to converge
under off-policy training. Our solution targets problems in reinforcement
learning where the action representation adds to the-curse-of-dimensionality;
that is, with continuous or large action sets, thus making it infeasible to
estimate state-action value functions (Q functions). Using state-value
functions helps to lift the curse and as a result naturally turn our
policy-gradient solution into classical Actor-Critic architecture whose Actor
uses state-value function for the update. Our algorithms, Gradient Actor-Critic
and Emphatic Actor-Critic, are derived based on the exact gradient of averaged
state-value function objective and thus are guaranteed to converge to its
optimal solution, while maintaining all the desirable properties of classical
Actor-Critic methods with no additional hyper-parameters. To our knowledge,
this is the first time that convergent off-policy learning methods have been
extended to classical Actor-Critic methods with function approximation.
