Learn Hard Problems During RL with Reference Guided Fine-tuning
This addresses the problem of sparse rewards in RL for mathematical reasoning, enabling more effective training on hard problems, though it is incremental as it builds on existing RL methods.
The paper tackled reward sparsity in reinforcement learning for mathematical reasoning by introducing Reference-Guided Fine-Tuning (ReGFT), which uses human-written reference solutions to synthesize positive trajectories, resulting in improved supervised accuracy, faster training, and higher final performance on benchmarks like AIME24, AIME25, and BeyondAIME.
Reinforcement learning (RL) for mathematical reasoning can suffer from reward sparsity: for challenging problems, LLM fails to sample any correct trajectories, preventing RL from receiving meaningful positive feedback. At the same time, there often exist human-written reference solutions along with the problem (e.g., problems from AoPS), but directly fine-tuning on these solutions offers no benefit because models often cannot imitate human proofs that lie outside their own reasoning distribution. We introduce Reference-Guided Fine-Tuning (ReGFT), a simple and effective method that utilizes human-written reference solutions to synthesize positive trajectories on hard problems and train on them before RL. For each problem, we provide the model with a partial reference solution and let it generate its own reasoning trace, ensuring the resulting trajectories remain in the model's reasoning space while still benefiting from reference guidance. Fine-tuning on these reference-guided trajectories increases the number of solvable problems and produces a checkpoint that receives more positive rewards during RL. Across three benchmarks (AIME24, AIME25, BeyondAIME), ReGFT consistently improves supervised accuracy, accelerates DAPO training, and raises the final performance plateau of RL. Our results show that ReGFT effectively overcomes reward sparsity and unlocks stronger RL-based mathematical reasoning.