  The policy gradient theorem gives a convenient form of the policy gradient in
terms of three factors: an action value, a gradient of the action likelihood,
and a state distribution involving discounting called the \emph{discounted
stationary distribution}. But commonly used on-policy methods based on the
policy gradient theorem ignores the discount factor in the state distribution,
which is technically incorrect and may even cause degenerate learning behavior
in some environments. An existing solution corrects this discrepancy by using
$\gamma^t$ as a factor in the gradient estimate. However, this solution is not
widely adopted and does not work well in tasks where the later states are
similar to earlier states. We introduce a novel distribution correction to
account for the discounted stationary distribution that can be plugged into
many existing gradient estimators. Our correction circumvents the performance
degradation associated with the $\gamma^t$ correction with a lower variance.
Importantly, compared to the uncorrected estimators, our algorithm provides
improved state emphasis to evade suboptimal policies in certain environments
and consistently matches or exceeds the original performance on several OpenAI
gym and DeepMind suite benchmarks.
