# Reinforcement-aware Knowledge Distillation for LLM Reasoning

arXiv: https://arxiv.org/abs/2602.22495 · HTML: https://mlsanity.com/paper/2602.22495/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 52 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)

## Built on by (most cited first, 30 of 35)

- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents](https://mlsanity.com/paper/2604.10674/) (2026)
- [SCOPE: Signal-Calibrated On-Policy Distillation Enhancement with Dual-Path Adaptive Weighting](https://mlsanity.com/paper/2604.10688/) (2026)
- [HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2603.23871/) (2026)
- [Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation](https://mlsanity.com/paper/2604.13010/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning](https://mlsanity.com/paper/2605.13255/) (2026)
- [Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training](https://mlsanity.com/paper/2605.12483/) (2026)
- [Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR](https://mlsanity.com/paper/2609.04108/) (2026)
- [Multi-Rollout On-Policy Distillation via Peer Successes and Failures](https://mlsanity.com/paper/2605.12652/) (2026)
- [Beyond SFT-to-RL: Pre-alignment via Black-Box On-Policy Distillation for Multimodal RL](https://mlsanity.com/paper/2604.28123/) (2026)
- [Self-Distilled Policy Gradient](https://mlsanity.com/paper/2606.04036/) (2026)
- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)
- [Group-Reflective Self-Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.28076/) (2026)
- [ADWIN: Adaptive Windows for Horizon-Aware On-Policy Distillation](https://mlsanity.com/paper/2605.28396/) (2026)
- [Lightning OPD 2.0: Mitigating Style Bias in Cross-Teacher On-Policy Distillation for Large Reasoning Models](https://mlsanity.com/paper/2607.28449/) (2026)
- [When Teachers Mislead: Spurious-Signal-Aware On-Policy Distillation](https://mlsanity.com/paper/2608.03632/) (2026)
- [RISE: Recursive Improvement via Self-Extrapolating Policy Distillation](https://mlsanity.com/paper/2609.05295/) (2026)
- [RewardFlow: Topology-Aware Reward Propagation on State Graphs for Agentic RL with Large Language Models](https://mlsanity.com/paper/2603.18859/) (2026)
- [Zone of Proximal Policy Optimization: Teacher in Prompts, Not Gradients](https://mlsanity.com/paper/2606.18216/) (2026)
- [OPDSearch+: On-Policy Distillation with RL Refinement for Search-Augmented Reasoning](https://mlsanity.com/paper/2608.24310/) (2026)
- [Structured Role-Aware Policy Optimization for Multimodal Reasoning](https://mlsanity.com/paper/2605.07274/) (2026)
- [Eliciting Weak-to-Strong Generalization with On-Policy Reverse Distillation](https://mlsanity.com/paper/2609.08798/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [DenoiseRL: Bootstrapping Reasoning Models to Recover from Noisy Prefixes](https://mlsanity.com/paper/2605.28421/) (2026)
- [PathRouter: Aligning Rewards with Retrieval Quality in Agentic Graph Retrieval-Augmented Generation](https://mlsanity.com/paper/2606.16409/) (2026)
- [ARKD: Adaptive Reinforcement Learning-Guided Bidirectional KL Divergence Distillation for Text Generation](https://mlsanity.com/paper/2606.29869/) (2026)
- [Distill Where the Student Goes: Teacher-Regularized RL for English-Evidence Cross-Lingual RAG](https://mlsanity.com/paper/2607.02966/) (2026)
- [OptiAgent: End-to-End Optimization Modeling via Multi-Agent Iterative Refinement](https://mlsanity.com/paper/2607.05346/) (2026)
- [AdaStop: Cost-Aware Early Stopping for DNN Test Selection](https://mlsanity.com/paper/2607.05461/) (2026)

## Abstract (arXiv)

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.