The Best of N Worlds: Aligning Reinforcement Learning with Best-of-N Sampling via max@k Optimisation

• URL: http://arxiv.org/abs/2510.23393v1
• Date: Mon, 27 Oct 2025 14:47:30 GMT
• Title: The Best of N Worlds: Aligning Reinforcement Learning with Best-of-N Sampling via max@k Optimisation
• Authors: Farid Bagirov, Mikhail Arkhipov, Ksenia Sycheva, Evgeniy Glukhov, Egor Bogomolov,
• Abstract summary: We focus on optimizing the max@k metric, a continuous generalization of pass@k.<n>We extend our derivations to the off-policy updates, a common element in modern RLVR algorithms, that allows better sample efficiency.
• Score: 2.5960620227199342
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The application of Reinforcement Learning with Verifiable Rewards (RLVR) to mathematical and coding domains has demonstrated significant improvements in the reasoning and problem-solving abilities of Large Language Models. Despite its success in single generation problem solving, the reinforcement learning fine-tuning process may harm the model's exploration ability, as reflected in decreased diversity of generations and a resulting degradation of performance during Best-of-N sampling for large N values. In this work, we focus on optimizing the max@k metric, a continuous generalization of pass@k. We derive an unbiased on-policy gradient estimate for direct optimization of this metric. Furthermore, we extend our derivations to the off-policy updates, a common element in modern RLVR algorithms, that allows better sample efficiency. Empirically, we show that our objective effectively optimizes max@k metric in off-policy scenarios, aligning the model with the Best-of-N inference strategy.

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