  Reinforcement learning (RL) has been widely used in training large language
models (LLMs) for preventing unexpected outputs, eg reducing harmfulness and
errors. However, existing RL methods mostly adopt the instance-level reward,
which is unable to provide fine-grained supervision for complex reasoning
tasks, and can not focus on the few key tokens that lead to the incorrectness.
To address it, we propose a new RL method named RLMEC that incorporates a
generative model as the reward model, which is trained by the erroneous
solution rewriting task under the minimum editing constraint, and can produce
token-level rewards for RL training. Based on the generative reward model, we
design the token-level RL objective for training and an imitation-based
regularization for stabilizing RL process. And the both objectives focus on the
learning of the key tokens for the erroneous solution, reducing the effect of
other unimportant tokens. The experiment results on mathematical tasks and
question-answering tasks have demonstrated the effectiveness of our approach.
Our code and data are available at https://github.com/RUCAIBox/RLMEC.
