  Traditional off-policy actor-critic Reinforcement Learning (RL) algorithms
learn value functions of a single target policy. However, when value functions
are updated to track the learned policy, they forget potentially useful
information about old policies. We introduce a class of value functions called
Parameter-Based Value Functions (PBVFs) whose inputs include the policy
parameters. They can generalize across different policies. PBVFs can evaluate
the performance of any policy given a state, a state-action pair, or a
distribution over the RL agent's initial states. First we show how PBVFs yield
novel off-policy policy gradient theorems. Then we derive off-policy
actor-critic algorithms based on PBVFs trained by Monte Carlo or Temporal
Difference methods. We show how learned PBVFs can zero-shot learn new policies
that outperform any policy seen during training. Finally our algorithms are
evaluated on a selection of discrete and continuous control tasks using shallow
policies and deep neural networks. Their performance is comparable to
state-of-the-art methods.
