What should post-training optimize? A test-time scaling law perspective

arXiv:2605.10716v1 Announce Type: new Abstract: Large language models are increasingly deployed with test-time strategies: sample N responses, score them with a reward model or verifier, and return the best. This deployment rule exposes a mismatch in post-training: standard objectives optimize the mean reward of a single response, whereas best-of-N performance is governed by the upper tail of the reward distribution. Recent test-time-aware objectives partly address this mismatch, but typically assume that training can use the same per-prompt rollout budget as deployment, which is impractical when post-training must cover many prompts while deployment can allocate much larger per-prompt test-time compute. We study this budget-mismatch regime, where only mll N per-prompt rollouts are available during training but the target objective is best-of-N deployment. Under structural assumptions on the reward tails, we show that the policy gradient of the best-of-N objective can be approximated from a much smaller rollout group by extrapolating upper-tail statistics. This yields a family of Tail-Extrapolated estimators for best-of-N-oriented post-training: a simple direct estimator, Tail-Extrapolated Advantage (TEA), and a fixed-order debiased Prefix-TEA estimator based on moment cancellation. Experiments on instruction-following tasks show that TEA and Prefix-TEA improve best-of-N performance across different language models, reward models and datasets under various training and test-time budget settings.

Source: arXiv cs.LG | 2026-05-12