  Rejection sampling is a common tool for low dimensional problems ($d \leq
2$), often touted as an "easy" way to obtain valid samples from a distribution
$f(\cdot)$ of interest. In practice it is non-trivial to apply, often requiring
considerable mathematical effort to devise a good proposal distribution
$g(\cdot)$ and select a supremum $C$. More advanced samplers require additional
mathematical derivations, limitations on $f(\cdot)$, or even cross-validation,
making them difficult to apply. We devise a new approximate baseline approach
to rejection sampling that works with less information, requiring only a
differentiable $f(\cdot)$ be specified, making it easier to use. We propose a
new approach to rejection sampling by refining a parameterized proposal
distribution with a loss derived from the acceptance threshold. In this manner
we obtain comparable or better acceptance rates on current benchmarks by up to
$7.3\times$, while requiring no extra assumptions or any derivations to use:
only a differentiable $f(\cdot)$ is required. While approximate, the results
are correct with high probability, and in all tests pass a distributional
check. This makes our approach easy to use, reproduce, and efficacious.
