# HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation

arXiv: https://arxiv.org/abs/2603.23871 · HTML: https://mlsanity.com/paper/2603.23871/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-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, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [The Lipschitz Constant of Self-Attention](https://mlsanity.com/paper/2006.04710/) (2020)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Scaf-GRPO: Scaffolded Group Relative Policy Optimization for Enhancing LLM Reasoning](https://mlsanity.com/paper/2510.19807/) (2025)
- [No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping](https://mlsanity.com/paper/2509.21880/) (2025)
- [KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning](https://mlsanity.com/paper/2506.02208/) (2025)
- [RLEP: Reinforcement Learning with Experience Replay for LLM Reasoning](https://mlsanity.com/paper/2507.07451/) (2025)
- [The Choice of Divergence: A Neglected Key to Mitigating Diversity Collapse in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2509.07430/) (2025)
- [VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2509.19803/) (2025)
- [Reinforcement-aware Knowledge Distillation for LLM Reasoning](https://mlsanity.com/paper/2602.22495/) (2026)
- [Improving RL Exploration for LLM Reasoning through Retrospective Replay](https://mlsanity.com/paper/2504.14363/) (2025)
- [Don't Tell the Answer, Truly Guide the Reasoning During RL Rollouts](https://mlsanity.com/paper/2510.09388/) (2025)
- [EvoCoT: Overcoming the Exploration Bottleneck in Reinforcement Learning](https://mlsanity.com/paper/2508.07809/) (2025)

## Built on by (most cited first, 30 of 42)

- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Self-Distilled Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.15155/) (2026)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [Prune-OPD: Efficient and Reliable On-Policy Distillation for Long-Horizon Reasoning](https://mlsanity.com/paper/2605.07804/) (2026)
- [GenEvolve: Self-Evolving Image Generation Agents via Tool-Orchestrated Visual Experience Distillation](https://mlsanity.com/paper/2605.21605/) (2026)
- [OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning](https://mlsanity.com/paper/2605.12400/) (2026)
- [Prefix Teach, Suffix Fade: Local Teachability Collapse in Strong-to-Weak On-Policy Distillation](https://mlsanity.com/paper/2605.13643/) (2026)
- [Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning](https://mlsanity.com/paper/2605.11458/) (2026)
- [Preference-Based Self-Distillation: Beyond KL Matching via Reward Regularization](https://mlsanity.com/paper/2605.05040/) (2026)
- [OPRD: On-Policy Representation Distillation](https://mlsanity.com/paper/2606.06021/) (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)
- [Skill0.5: Joint Skill Internalization and Utilization for Out-of-Distribution Generalization in Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.28424/) (2026)
- [H-OPD: Confidence Aware Heterogeneous Multi-Teacher Multimodal On-policy Distillation](https://mlsanity.com/paper/2607.02592/) (2026)
- [CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization](https://mlsanity.com/paper/2605.19436/) (2026)
- [On-Policy Distillation with Best-of-N Teacher Rollout Selection](https://mlsanity.com/paper/2605.09725/) (2026)
- [AVSD: Adaptive-View Self-Distillation by Balancing Consensus and Teacher-Specific Privileged Signals](https://mlsanity.com/paper/2605.20643/) (2026)
- [OPSD Compresses What RLVR Teaches: A Post-RL Compaction Stage for Reasoning Models](https://mlsanity.com/paper/2605.06188/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)
- [SocraticPO: Policy Optimization via Interactive Guidance](https://mlsanity.com/paper/2606.09887/) (2026)
- [Learning from Own Solutions: Self-Conditioned Credit Assignment for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2606.18810/) (2026)
- [CAST: Non-Privileged Clipped Asymmetric Self-Teaching with Advantage Flipping for GRPO](https://mlsanity.com/paper/2606.00172/) (2026)
- [RetireOPD: Self-Retiring On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2609.20784/) (2026)
- [Restoring the Sweet Spot: Pass-Rate Weighted Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.27765/) (2026)
- [Teaching the Way, Not the Answer: Privileged Tutoring Distillation for Multimodal Policy Optimization](https://mlsanity.com/paper/2606.07000/) (2026)
- [Self-Distillation Policy Optimization via Visual Feedback: Bridging Code and Visual Artifacts](https://mlsanity.com/paper/2606.10334/) (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)

## Abstract (arXiv)

Large language models trained with reinforcement learning (RL) for mathematical reasoning face a fundamental challenge: on problems the model cannot solve at all - "cliff" prompts - the RL gradient vanishes entirely, preventing any learning signal from reaching these failure modes. We introduce Hybrid Distillation Policy Optimization (HDPO), which augments standard RL with privileged self-distillation targeting cliff prompts. On each training step, HDPO identifies prompts where all rollouts fail, generates privileged rollouts by providing the model with ground-truth information, filters for correct solutions, and distills the teacher's token-level distribution into the student. Because teacher and student share the same weights - differing only in their input - the realizability gap is provably bounded, unlike cross-model distillation. We prove that R=1 filtered privileged generation recovers the optimal KL-regularized RL policy in the hard-threshold limit. Experiments on OpenMathInstruct-2 with Qwen2.5-Math-1.5B-Instruct show that HDPO consistently improves coverage metrics (pass@4 by +0.8-1.1%, pass@8 by +0.4-1.7%) while maintaining greedy accuracy, with the distillation weight lambda providing direct control over the exploration-exploitation tradeoff.