# Recovering Off-Policy Supervision for Speculative Decoding

arXiv: https://arxiv.org/abs/2609.38795 · HTML: https://mlsanity.com/paper/2609.38795/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 33 of its 39 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 33)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [DocVQA: A Dataset for VQA on Document Images](https://mlsanity.com/paper/2007.00398/) (2020)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [ShareGPT4V: Improving Large Multi-Modal Models with Better Captions](https://mlsanity.com/paper/2311.12793/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [ALLaVA: Harnessing GPT4V-Synthesized Data for Lite Vision-Language Models](https://mlsanity.com/paper/2402.11684/) (2024)
- [DFlash: Block Diffusion for Flash Speculative Decoding](https://mlsanity.com/paper/2602.06036/) (2026)
- [Learning Harmonized Representations for Speculative Sampling](https://mlsanity.com/paper/2408.15766/) (2024)
- [PARD: Accelerating LLM Inference with Low-Cost PARallel Draft Model Adaptation](https://mlsanity.com/paper/2504.18583/) (2025)
- [Direct Alignment of Draft Model for Speculative Decoding with Chat-Fine-Tuned LLMs](https://mlsanity.com/paper/2403.00858/) (2024)
- [ParallelSpec: Parallel Drafter for Efficient Speculative Decoding](https://mlsanity.com/paper/2410.05589/) (2024)
- [ViSpec: Accelerating Vision-Language Models with Vision-Aware Speculative Decoding](https://mlsanity.com/paper/2509.15235/) (2025)
- [Falcon: Faster and Parallel Inference of Large Language Models through Enhanced Semi-Autoregressive Drafting and Custom-Designed Decoding Tree](https://mlsanity.com/paper/2412.12639/) (2024)
- [DREAM: Drafting with Refined Target Features and Entropy-Adaptive Cross-Attention Fusion for Multimodal Speculative Decoding](https://mlsanity.com/paper/2505.19201/) (2025)
- [Speculative Decoding Reimagined for Multimodal Large Language Models](https://mlsanity.com/paper/2505.14260/) (2025)
- [Training Domain Draft Models for Speculative Decoding: Best Practices and Insights](https://mlsanity.com/paper/2503.07807/) (2025)
- [PARD-2: Target-Aligned Parallel Draft Model for Dual-Mode Speculative Decoding](https://mlsanity.com/paper/2605.08632/) (2026)

## Abstract (arXiv)

Block drafters for speculative decoding are commonly trained on corpora written by external models, where a single off-policy token invalidates supervision for all subsequent slots in a block. Existing approaches discard these divergent slots, resulting in severe supervision loss. To resolve this problem while preserving the training corpus, we propose a rollout-based training framework that recovers full supervision through two complementary components. The first component, Anchor-Label Relabelling (ALR), replaces corpus labels with distributions from greedy target rollouts, restoring valid supervision across all predicted slots. The second component, In-Rollout Anchors (IRA), places draft blocks directly inside these rollouts to expose the drafter to target-generated context, reusing precomputed rollout features at no additional target cost. Across fixed vision-language and text corpora, our framework increases greedy accepted length by up to 36.5% over DFlash and consistently outperforms erasing baselines. Notably, a single epoch of our method surpasses the best erase schedules. After three epochs, it matches the acceptance length of training on target-regenerated responses. These results show that our framework provides an effective and compute-efficient approach for training speculative drafters on fixed corpora without modifying the original text. Code is available at https://github.com/js-lee-AI/ALR-IRA.