KnowRL: Boosting LLM Reasoning via Reinforcement Learning with Minimal-Sufficient Knowledge Guidance

TL;DR

KnowRL introduces a minimal-sufficient knowledge guidance framework for reinforcement learning in large language models, significantly improving reasoning performance by optimizing guidance construction.

Contribution

It proposes a novel approach to guidance design using atomic knowledge points and a constrained subset search, enhancing RL training efficiency and effectiveness.

Findings

KnowRL outperforms strong RL and hinting baselines on eight reasoning benchmarks.

It achieves 70.08% accuracy without KP hints, surpassing previous models.

With selected KPs, it reaches 74.16% accuracy, setting a new state of the art.

Abstract

RLVR improves reasoning in large language models, but its effectiveness is often limited by severe reward sparsity on hard problems. Recent hint-based RL methods mitigate sparsity by injecting partial solutions or abstract templates, yet they typically scale guidance by adding more tokens, which introduce redundancy, inconsistency, and extra training overhead. We propose \textbf{KnowRL} (Knowledge-Guided Reinforcement Learning), an RL training framework that treats hint design as a minimal-sufficient guidance problem. During RL training, KnowRL decomposes guidance into atomic knowledge points (KPs) and uses Constrained Subset Search (CSS) to construct compact, interaction-aware subsets for training. We further identify a pruning interaction paradox -- removing one KP may help while removing multiple such KPs can hurt -- and explicitly optimize for robust subset curation under this dependency structure. We train KnowRL-Nemotron-1.5B from OpenMath-Nemotron-1.5B. Across eight reasoning benchmarks at the 1.5B scale, KnowRL-Nemotron-1.5B consistently outperforms strong RL and hinting baselines. Without KP hints at inference, KnowRL-Nemotron-1.5B reaches 70.08 average accuracy, already surpassing Nemotron-1.5B by +9.63 points; with selected KPs, performance improves to 74.16, establishing a new state of the art at this scale. The model, curated training data, and code are publicly available at https://github.com/Hasuer/KnowRL.