LAND: Learning an Adaptive Number of Draws for Bayesian Best-of-N Selection

Abstract

Best-of-N decoding improves generation quality by sampling multiple candidates and selecting the best, but it allocates equal compute to sources regardless of how much they benefit from additional sampling: the expected benefit is small for sources with low-variance score distributions and potentially much larger for those with high-variance distributions. To address this shortcoming, we propose LAND (Learning an Adaptive Number of Draws), which dynamically allocates samples according to their posterior-predictive marginal value. LAND learns a discrete empirical mixture of source-conditioned score distributions from calibration data, updates its belief about a source as completion scores are observed, and stops sampling when the expected improvement of another draw falls below a shared compute price. Across machine-translation experiments with multiple models and language pairs, LAND achieves better MetricX scores than fixed best-of-N at matched average compute. Conversely, at matched translation quality, LAND requires approximately 20-40% fewer candidate generations. Adaptive allocation therefore provides a simple way to retain the benefits of best-of-N while substantially improving its compute efficiency.