# RELAY: Selective Self-Distillation with Adaptive Hand-off for Rubric-Based Reinforcement Learning

arXiv: https://arxiv.org/abs/2610.17623 · HTML: https://mlsanity.com/paper/2610.17623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 13 Oct 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, 30 of 36)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Checklists Are Better Than Reward Models For Aligning Language Models](https://mlsanity.com/paper/2507.18624/) (2025)
- [DR Tulu: Reinforcement Learning with Evolving Rubrics for Deep Research](https://mlsanity.com/paper/2511.19399/) (2025)
- [Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?](https://mlsanity.com/paper/2603.24472/) (2026)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)
- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [RubricHub: A Comprehensive and Highly Discriminative Rubric Dataset via Automated Coarse-to-Fine Generation](https://mlsanity.com/paper/2601.08430/) (2026)
- [ResearchQA: Evaluating Scholarly Question Answering at Scale Across 75 Fields with Survey-Mined Questions and Rubrics](https://mlsanity.com/paper/2509.00496/) (2025)
- [Online Rubrics Elicitation from Pairwise Comparisons](https://mlsanity.com/paper/2510.07284/) (2025)
- [The Many Faces of On-Policy Distillation: Pitfalls, Mechanisms, and Fixes](https://mlsanity.com/paper/2605.11182/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [LLMEval-Med: A Real-world Clinical Benchmark for Medical LLMs with Physician Validation](https://mlsanity.com/paper/2506.04078/) (2025)
- [STEPS: Selective On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.10194/) (2026)
- [Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR](https://mlsanity.com/paper/2605.10781/) (2026)
- [Rubric-Guided Self-Distillation: Post-Training Without Rubric Verifiers](https://mlsanity.com/paper/2606.12507/) (2026)
- [Rethinking Reward Supervision: Rubric-Conditioned Self-Distillation](https://mlsanity.com/paper/2606.19327/) (2026)
- [PAPO: Stabilizing Rubric Integration Training via Decoupled Advantage Normalization](https://mlsanity.com/paper/2603.26535/) (2026)
- [Distill Where You Fail: Recovering Learning Signals of Negative RL-Groups from Adaptive Teacher Guidance](https://mlsanity.com/paper/2608.00782/) (2026)
- [Sequential Beats Joint: On the Interplay between On-Policy Distillation and RLVR](https://mlsanity.com/paper/2609.04108/) (2026)
- [Rubrics to Tokens: Bridging Response-level Rubrics and Token-level Rewards in Instruction Following Tasks](https://mlsanity.com/paper/2604.02795/) (2026)
- [Alternating Reinforcement Learning with Contextual Rubric Rewards: Beyond the Scalarization Strategy](https://mlsanity.com/paper/2603.15646/) (2026)
- [CriPO: Enhancing Rubric-based RL via Self-Distillation](https://mlsanity.com/paper/2607.18082/) (2026)

## Abstract (arXiv)

Rubric-based reinforcement learning grades a response against many written criteria but collapses them into one reward, which discards the detail the rubric carries and gives no GRPO reward gradient when a group's responses tie. A frozen teacher that reads the rubric as privileged context provides token-level supervision, but we observe an early plateau in the gains over GRPO. RELAY uses advantages and rewards to select positive-advantage and low-scoring zero-advantage rollouts, and monitors the distillation loss to decide when to retire the teacher. Stage 1 combines selective distillation from a frozen teacher with GRPO; a plateau detector then removes the teacher, and Stage 2 continues with GRPO alone. Calibrated on one model-domain pair and reused unchanged in three others, the plateau detector fires between steps 122 and 171. RELAY scores highest in-domain among the compared methods in all four settings, ahead of GRPO on RaR-Medicine by 4.62 points with Qwen3-1.7B and 6.02 with Qwen3-4B. On Qwen3-1.7B/Medicine, removing the teacher from a shared checkpoint outperforms keeping, weakening or refreshing it. Distilling selected rollouts covering about half the response tokens also outperforms distilling all rollouts at a matched average coefficient.