Policy gradient methods are widely used for control in reinforcement learning, particularly for the continuous action setting. There have been a host of theoretically sound algorithms proposed for the on-policy setting, due to the existence of the policy gradient theorem which provides a simplified form for the gradient. In off-policy learning, however, where the behaviour policy is not necessarily attempting to learn and follow the optimal policy for the given task, the existence of such a theorem has been elusive. In this work, we solve this open problem by providing the first off-policy policy gradient theorem. The key to the derivation is the use of $emphatic$ $weightings$. We develop a new actor-critic algorithm$\unicode{x2014}$called Actor Critic with Emphatic weightings (ACE)$\unicode{x2014}$that approximates the simplified gradients provided by the theorem. We demonstrate in a simple counterexample that previous off-policy policy gradient methods$\unicode{x2014}$particularly OffPAC and DPG$\unicode{x2014}$converge to the wrong solution whereas ACE finds the optimal solution.

本文提出了第一个适用于off-policy learning的policy gradient定理，并通过使用emphatic weightings导出了简化的梯度公式，并使用Actor Critic with Emphatic weightings (ACE)算法验证了该定理的正确性。

使用强调加权的离线策略梯度定理