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KETCHUP: K-Step Return Estimation for Sequential Knowledge Distillation

Jiabin Fan, Guoqing Luo, Michael Bowling, Lili Mou

TL;DR

KETCHUP introduces a $K$-step return induction for RL-based knowledge distillation in text generation, deriving a multi-step Bellman-guided learning signal to reduce gradient variance. By constructing $\hat{G}_t$ from $K$-step reward blocks and using the student policy to propagate states, the method achieves variance reduction with a controllable bias, performing well across XSum, Europarl EN-NL, and GSM8K. Empirical results show improved RL return and NLP metrics, with moderate $K$ (2–8) offering the best balance between bias and variance, and LLM-based evaluation corroborating human-aligned improvements. The approach promises more stable and effective RL-based KD in large language model settings, highlighting a practical path for enhancing distillation in resource-constrained deployments.

Abstract

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.

KETCHUP: K-Step Return Estimation for Sequential Knowledge Distillation

TL;DR

KETCHUP introduces a -step return induction for RL-based knowledge distillation in text generation, deriving a multi-step Bellman-guided learning signal to reduce gradient variance. By constructing from -step reward blocks and using the student policy to propagate states, the method achieves variance reduction with a controllable bias, performing well across XSum, Europarl EN-NL, and GSM8K. Empirical results show improved RL return and NLP metrics, with moderate (2–8) offering the best balance between bias and variance, and LLM-based evaluation corroborating human-aligned improvements. The approach promises more stable and effective RL-based KD in large language model settings, highlighting a practical path for enhancing distillation in resource-constrained deployments.

Abstract

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.
Paper Structure (30 sections, 1 theorem, 21 equations, 3 figures, 7 tables, 1 algorithm)

This paper contains 30 sections, 1 theorem, 21 equations, 3 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. RL Formulation of Text Generation
  4. Our $K$etchup Method
  5. Bias and Variance Analysis
  6. Experiments
  7. Settings
  8. Tasks, Datasets, and Metrics.
  9. Implementation Details.
  10. Competing Methods.
  11. Main Results
  12. Return in RL.
  13. NLP Task Performance.
  14. In-Depth Analyses
  15. Variance and bias analysis.
  16. ...and 15 more sections

Key Result

Theorem 1

Let $G_t$ be the actual return and $\hat{G}_t$ be the $K$-step approximate return for some sequences sampled from the student policy $\pi$. Assuming that the state--action--reward tuples $(s_t, a_t, r_t)$ are iid drawn at different steps, we have:

Figures (3)

  • Figure 1: Average predicted return vs Approaches.
  • Figure 2: Variance and bias with different $K$ values.
  • Figure 3: Learning curves with different $K$ values and model sizes, where the $x$-axis is the number of training steps.

Theorems & Definitions (3)

  • Theorem 1: Variance Reduction via $K$-Step Return
  • proof
  • proof