Reinforcement learning applied to large language models (LLMs) for reasoning
tasks is often bottlenecked by unstable gradient estimates due to fixed and
uniform sampling of responses across prompts. Prior work such as GVM-RAFT
addresses this by dynamically allocating inference budget per prompt to
minimize stochastic gradient variance under a budget constraint. Inspired by
this insight, we propose Reinforce-Ada, an adaptive sampling framework for
online RL post-training of LLMs that continuously reallocates sampling effort
to the prompts with the greatest uncertainty or learning potential. Unlike
conventional two-stage allocation methods, Reinforce-Ada interleaves estimation
and sampling in an online successive elimination process, and automatically
stops sampling for a prompt once sufficient signal is collected. To stabilize
updates, we form fixed-size groups with enforced reward diversity and compute
advantage baselines using global statistics aggregated over the adaptive
sampling phase. Empirical results across multiple model architectures and
reasoning benchmarks show that Reinforce-Ada accelerates convergence and
improves final performance compared to GRPO, especially when using the balanced
sampling variant. Our work highlights the central role of variance-aware,
adaptive data curation in enabling efficient and reliable reinforcement
learning for reasoning-capable LLMs. Code is available at
https://github.com/RLHFlow/Reinforce-Ada.