Parallelized Acquisition for Active Learning using Monte Carlo Sampling

Abstract

Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the posterior. Recent attention has been directed towards the use of emulators of the posterior based on Gaussian Process (GP) regression combined with active sampling to achieve comparable precision with far fewer costly likelihood evaluations. Key to this approach is the batched acquisition of proposals, so that the true posterior can be evaluated in parallel. This is usually achieved via sequential maximization of the highly multimodal acquisition function. Unfortunately, this approach parallelizes poorly and is prone to getting stuck in local maxima. Our approach addresses this issue by generating nearly-optimal batches of candidates using an almost-embarrassingly parallel Nested Sampler on the mean prediction of the GP. The resulting nearly-sorted Monte Carlo sample is used to generate a batch of candidates ranked according to their sequentially conditioned acquisition function values at little cost. The final sample can also be used for inferring marginal quantities. Our proposed implementation (NORA) demonstrates comparable accuracy to sequential conditioned acquisition optimization and efficient parallelization in various synthetic and cosmological inference problems.