  In generative models with obscured likelihood, Approximate Bayesian
Computation (ABC) is often the tool of last resort for inference. However, ABC
demands many prior parameter trials to keep only a small fraction that passes
an acceptance test. To accelerate ABC rejection sampling, this paper develops a
self-aware framework that learns from past trials and errors. We apply
recursive partitioning classifiers on the ABC lookup table to sequentially
refine high-likelihood regions into boxes. Each box is regarded as an arm in a
binary bandit problem treating ABC acceptance as a reward. Each arm has a
proclivity for being chosen for the next ABC evaluation, depending on the prior
distribution and past rejections. The method places more splits in those areas
where the likelihood resides, shying away from low-probability regions destined
for ABC rejections. We provide two versions: (1) ABC-Tree for posterior
sampling, and (2) ABC-MAP for maximum a posteriori estimation. We demonstrate
accurate ABC approximability at much lower simulation cost. We justify the use
of our tree-based bandit algorithms with nearly optimal regret bounds. Finally,
we successfully apply our approach to the problem of masked image
classification using deep generative models.
