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arXiv · 2512.23097

A Note on Hybrid Online Reinforcement and Imitation Learning for LLMs: Formulations and Algorithms

Yingru Li·Ziniu Li·Jiacai Liu
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Abstract

We present a unified framework for Large Language Model (LLM) fine-tuning that integrates Imitation Learning and Reinforcement Learning. By analyzing the gradient of a composite objective combining trajectory-level KL divergence with task rewards, we derive a natural decomposition into two components: (1) an analytically computable Dense Gradient for token-level imitation, and (2) a Monte Carlo estimated Sparse Gradient for long-horizon reward optimization. The Dense Gradient admits a closed-form logit-level formula, enabling efficient GPU implementation.

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Yingru Li, Ziniu Li, Jiacai Liu. 2025-12-28. A Note on Hybrid Online Reinforcement and Imitation Learning for LLMs: Formulations and Algorithms. https://arxiv.org/abs/2512.23097

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