KnowRL: Boosting LLM Reasoning via Reinforcement Learning with Minimal-Sufficient Knowledge Guidance
For researchers working on LLM reasoning, KnowRL provides a method to mitigate reward sparsity in RL training by injecting minimal-sufficient knowledge guidance, improving performance without scaling hint tokens.
KnowRL introduces a reinforcement learning framework that treats hint design as a minimal-sufficient guidance problem, using Constrained Subset Search to construct compact knowledge point subsets. It achieves 70.08% average accuracy across eight reasoning benchmarks at 1.5B scale, surpassing the baseline by +9.63 points, and reaches 74.16% with selected hints, setting a new state of the art.
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.