Best-of-K Objectives: Optimizing for Pass@K and Max@K

At inference time, neural solvers typically sample multiple candidate solutions and keep the best one. I am interested in training directly for these best-of-K settings by optimizing Pass@K and Max@K objectives, so that the training signal matches how models are actually deployed. This work explores objective design, variance reduction, and the trade-off between solution diversity and per-sample quality.