A minimax near-optimal algorithm for adaptive rejection sampling
This addresses the efficiency issue in Monte-Carlo sampling for researchers and practitioners, offering a theoretical foundation where previous methods lacked guarantees.
The paper tackles the problem of high rejection rates in adaptive rejection sampling by introducing a new algorithm that guarantees a near-optimal rejection rate in a minimax sense, providing the first theoretical lower bound for this problem.
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However, without proper tuning, this technique implies a high rejection rate. Several methods have been explored to cope with this problem, based on the principle of adaptively estimating the density by a simpler function, using the information of the previous samples. Most of them either rely on strong assumptions on the form of the density, or do not offer any theoretical performance guarantee. We give the first theoretical lower bound for the problem of adaptive rejection sampling and introduce a new algorithm which guarantees a near-optimal rejection rate in a minimax sense.