Two of the leading approaches for model-free reinforcement learning are policy gradient methods and Q-learning methods. Q-learning methods can be effective and sample-efficient when they work, however, it is not well-understood why they work, since empirically, the Q-values they estimate are very inaccurate. A partial explanation may be that Q-learning methods are secretly implementing policy gradient updates: we show that there is a precise equivalence between Q-learning and policy gradient methods in the setting of entropy-regularized reinforcement learning, that "soft" (entropy-regularized) Q-learning is exactly equivalent to a policy gradient method. We also point out a connection between Q-learning methods and natural policy gradient methods. Experimentally, we explore the entropy-regularized versions of Q-learning and policy gradients, and we find them to perform as well as (or...