Reinforcement Learning-based Semi-supervised Knowledge Distillation with LLM-as-a-Judge

Reinforcement learning has emerged as a powerful paradigm for improving large language model (LLM) reasoning, where rollouts are sampled from the policy and reward signals computed on those rollouts are used to update the policy. However, in data-scarce scenarios, obtaining ground-truth labels to verify rollouts at scale often requires expensive human annotation or labor-intensive expert verification. For instance, evaluating mathematical proofs demands expert review, and open-ended question answering lacks definitive ground truth. When ground-truth labels are scarce, the effectiveness of reinforcement learning fine-tuning is constrained. Inspired by the success of semi-supervised learning in propagating labels from labeled to unlabeled samples, we propose MemReward, a graph-based experience memory framework that integrates reward propagation directly into online policy optimization. MemReward stores rollouts (thinking processes and final answers) from an initial LLM policy as nodes in a heterogeneous graph connected by similarity and structural edges, over which a GNN propagates rewards from labeled to unlabeled rollouts. To train such a framework, we first warm up the GNN on labeled rollouts to predict rewards via heterogeneous aggregation over query, thinking, and answer nodes. During online RL fine-tuning, unlabeled rollouts are attached to the graph by query similarity, and the GNN predicts their rewards, yielding a hybrid reward acquisition strategy that combines ground-truth and GNN-predicted rewards. Experiments on Qwen2.5-1.5B and 3B in mathematics, question answering, and code generation demonstrate that MemReward, with ground-truth rewards on only 20% of rollouts, achieves 96.6% of Oracle performance on 1.5B and 97.3% on 3B, and closely approaches Oracle on out-of-domain tasks.

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

For the development of Large language models (LLMs), recent approaches to generating pseudo intermediate reasoning have shown remarkable progress. But they typically rely on large numbers of correctly annotated answers to assess reasoning quality. This paper presents a semi-supervised framework that scales reasoning learning from minimal supervision, turning reasoning verification itself into a data creation mechanism. We train a lightweight reasoning-correctness classifier on only a few labeled samples, which judges whether intermediate reasoning traces generated by an LLM are valid. Furthermore, an entropy-based confidence threshold filters out unreliable samples, and the remaining high-confidence reasoning traces are used to fine-tune the model. Experiments on Verifiable Math Problems (Orca-Math subset) and Question Answering on Image Scene Graphs (GQA) with Visual Programming show that our method achieves accuracy comparable to using 10-15x more labeled data. Ablation analyses confirm that both the classifier and entropy filtering are essential for scalable and noise-resistant pseudo-labeling. By replacing expensive answer-level supervision with lightweight reasoning verification, our method provides a practical path toward constructing large-scale reasoning resources and paves the way for future autonomous reasoning systems that learn from minimal human input.