HeaPA: Difficulty-Aware Heap Sampling and On-Policy Query Augmentation for LLM Reinforcement Learning

RLVR has become a standard recipe for training LLMs on reasoning tasks with verifiable outcomes, but when rollout generation dominates the cost, efficiency hinges on which prompts are sampled and when. In practice, prompt pools are often static or only weakly coupled to policy progress, so uniform sampling fails to track the moving capability frontier and wastes rollouts on regions that are already solved or still unreachable. Prior methods improve efficiency via filtering, curricula, adaptive rollout allocation, or teacher guidance, but they often assume a fixed pool, which does not support stable on-policy pool growth, or they introduce additional teacher cost and latency. In this work, we propose HeaPA (Heap Sampling and On-Policy Query Augmentation), which maintains a bounded, evolving pool, tracks the frontier with heap-based boundary sampling, grows the pool via on-policy augmentation under lightweight asynchronous validation, and stabilizes correlated queries via topology-aware pool statistics re-estimation and controlled reinsertion. Across two training corpora, two training recipes, and seven benchmarks, HeaPA consistently improves accuracy and reaches target performance with fewer computations at comparable wall-clock time. Analyses attribute the gains to frontier-focused sampling and on-policy pool growth, with more pronounced improvements at mid-to-large model scales. Our training code is publicly available at https://github.com/horizon-llm/HeaPA.