  We present the first provably convergent two-timescale off-policy
actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is
the introduction of a new critic, the emphasis critic, which is trained via
Gradient Emphasis Learning (GEM), a novel combination of the key ideas of
Gradient Temporal Difference Learning and Emphatic Temporal Difference
Learning. With the help of the emphasis critic and the canonical value function
critic, we show convergence for COF-PAC, where the critics are linear and the
actor can be nonlinear.
