Tree Bandits for Generative Bayes

Sean O’Hagan, Jungeum Kim, Veronika Ročková

Journal of the American Statistical Association · Fri

DOI: 10.1080/01621459.2026.2658285

Abstract

In generative models with intractable likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter proposals to keep only the small fraction of them that meet the acceptance criterion. To accelerate ABC rejection sampling, this paper develops a self-aware framework that learns from past proposals: both acceptances and rejections. 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 acceptances and 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) MAP-Tree for maximum a posteriori estimation. We demonstrate accurate ABC approximability with reduced simulation cost. We justify the use of our tree-based bandit algorithms with nearly optimal regret bounds. Finally, we successfully apply our approach to posterior sampling in an epidemiological model and to model-based Bayesian optimization for alloy material discovery.

Keywords

ABC, Recursive Partitioning, Thompson Sampling, Likelihood-free MAP

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