  Importance sampling is a central idea underlying off-policy prediction in
reinforcement learning. It provides a strategy for re-weighting samples from a
distribution to obtain unbiased estimates under another distribution. However,
importance sampling weights tend to exhibit extreme variance, often leading to
stability issues in practice. In this work, we consider a broader class of
importance weights to correct samples in off-policy learning. We propose the
use of $\textit{value-aware importance weights}$ which take into account the
sample space to provide lower variance, but still unbiased, estimates under a
target distribution. We derive how such weights can be computed, and detail key
properties of the resulting importance weights. We then extend several
reinforcement learning prediction algorithms to the off-policy setting with
these weights, and evaluate them empirically.
