Title: The Best of N Worlds: Aligning Reinforcement Learning with Best-of-N Sampling via max@k Optimization
Primary area: reinforcement learning
Keywords: RLVR, Code Generation, pass@k

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.