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

KETCHUP: K-Step Return Estimation for Sequential Knowledge Distillation