Complementing reinforcement learning with SFT through logit averaging in the post training of LLMs

arXiv:2605.20555 · cs.LG, cs.AI · Submitted 2026-05-19 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-05-19

Updated: 2026-09-09

License: http://creativecommons.org/licenses/by/4.0/

The gist: We introduce a novel method that averages the logits of a frozen reference policy (e.g., SFT) and a trainable policy, and incorporate the method into Group Relative Policy Optimization (GRPO).

Terminology

• GRPO — 20× in this paper · explained in 6 episodes
• Accuracy — 13× in this paper · explained in 1 episode
• Reinforcement Learning — 11× in this paper · explained in 4 episodes
• Regularization — 10× in this paper · explained in 3 episodes
• Decode — 6× in this paper · explained in 2 episodes
• KL Regularization — 6× in this paper · explained in 2 episodes
• Distillation — 4× in this paper · explained in 2 episodes
• Verifiable Rewards — 3× in this paper · explained in 2 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Group Relative Policy Optimization — 2× in this paper
• Kullback Leibler — 2× in this paper
• Meeting of the Association for Computational Linguistics — 2× in this paper
• Reinforcement Learning with Verifiable Rewards — 2× in this paper
• Self-Distillation — 2× in this paper · explained in 7 episodes
• Verifier — 2× in this paper · explained in 2 episodes
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Continual Learning — 1× in this paper · explained in 2 episodes
• Edge AI — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• GRPO Objective — 1× in this paper · explained in 2 episodes
• Group Relative Policy Optimization (GRPO) — 1× in this paper · explained in 5 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• On-Policy Distillation — 1× in this paper · explained in 3 episodes
• Product of Experts — 1× in this paper
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Supervised Fine-Tuning (SFT) — 1× in this paper · explained in 8 episodes

Abstract

Sources

• Reinforcement Learning via Self-Distillation
• Tuning Language Models by Proxy
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Proximal Policy Optimization Algorithms
• DAPO: An Open-Source LLM Reinforcement Learning System at Scale
• Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning
• Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback
• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

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