# KETCHUP: K-Step Return Estimation for Sequential Knowledge Distillation

arXiv: https://arxiv.org/abs/2504.19024 · HTML: https://mlsanity.com/paper/2504.19024/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 49 of its 84 references that are in the map.
- First posted on arXiv 26 Apr 2025.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 30 of 49)

- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Can Large Language Models Be an Alternative to Human Evaluations?](https://mlsanity.com/paper/2305.01937/) (2023)
- [Patient Knowledge Distillation for BERT Model Compression](https://mlsanity.com/paper/1908.09355/) (2019)
- [Large Language Models Are Not Robust Multiple Choice Selectors](https://mlsanity.com/paper/2309.03882/) (2023)
- [Quantifying Generalization in Reinforcement Learning](https://mlsanity.com/paper/1812.02341/) (2018)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Teaching Small Language Models to Reason](https://mlsanity.com/paper/2212.08410/) (2022)
- [Adapted Large Language Models Can Outperform Medical Experts in Clinical Text Summarization](https://mlsanity.com/paper/2309.07430/) (2023)

## Built on by (most cited first, 3 of 3)

- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [RMB: Reward Model Boosting Mitigates Reward Hacking](https://mlsanity.com/paper/2609.33221/) (2026)

## Abstract (arXiv)

We propose a novel k-step return estimation method (called KETCHUP) for Reinforcement Learning(RL)-based knowledge distillation (KD) in text generation tasks. Our idea is to induce a K-step return by using the Bellman Optimality Equation for multiple steps. Theoretical analysis shows that this K-step formulation reduces the variance of the gradient estimates, thus leading to improved RL optimization especially when the student model size is large. Empirical evaluation on three text generation tasks demonstrates that our approach yields superior performance in both standard task metrics and large language model (LLM)-based evaluation. These results suggest that our K-step return induction offers a promising direction for enhancing RL-based KD in LLM research.