Optimal Budgeted Rejection Sampling for Generative Models
This work addresses a bottleneck in generative modeling by providing a more practical and integrated rejection sampling approach, which is incremental but offers specific gains for researchers and practitioners in machine learning.
The paper tackles the problem of rejection sampling methods for generative models being optimal only under unlimited budgets and independent of training, by proposing an Optimal Budgeted Rejection Sampling (OBRS) scheme that is provably optimal for any f-divergence with a given budget and an end-to-end training method to enhance performance, showing significant improvements in sample quality and diversity.
Rejection sampling methods have recently been proposed to improve the performance of discriminator-based generative models. However, these methods are only optimal under an unlimited sampling budget, and are usually applied to a generator trained independently of the rejection procedure. We first propose an Optimal Budgeted Rejection Sampling (OBRS) scheme that is provably optimal with respect to \textit{any} $f$-divergence between the true distribution and the post-rejection distribution, for a given sampling budget. Second, we propose an end-to-end method that incorporates the sampling scheme into the training procedure to further enhance the model's overall performance. Through experiments and supporting theory, we show that the proposed methods are effective in significantly improving the quality and diversity of the samples.