Automatically generating feedback via large language models (LLMs) in intelligent tutoring systems and online learning platforms has the potential to improve the learning outcomes of many students. However, both feedback generation and evaluation are challenging: feedback content has to be valid especially in subjects like math, which requires models to understand the problem, the solution, and where the student's error lies. Feedback also has to be pedagogically valid to reflect effective tutoring strategies, such as explaining possible misconceptions and encouraging the student, among other desirable features. In this work, we address both problems of automatically generating and evaluating feedback while considering both correctness and alignment. First, we propose a rubric for evaluating math feedback and show that GPT-4 is able to effectively use it to annotate human-written and LLM-generated feedback. Second, we propose a framework for feedback generation that optimizes both correctness and alignment using reinforcement learning (RL). Specifically, we use GPT-4's annotations to create preferences over feedback pairs in an augmented dataset for training via direct preference optimization (DPO). We show that our methods significantly increase the correctness and alignment of generated feedback with Llama 2, an open-source LLM, qualitatively analyze our generation and evaluation systems using case studies, and outline several areas for future work.

翻译：在智能辅导系统和在线学习平台中，利用大型语言模型自动生成反馈有望改善众多学生的学习成果。然而，反馈的生成与评估均面临挑战：反馈内容必须有效，尤其在数学等学科中，这要求模型理解问题、解题过程以及学生的错误所在。反馈还需符合教学法原则，以体现有效的辅导策略，例如解释可能的误解、鼓励学生等理想特征。本研究针对自动生成与评估反馈这两个问题，同时兼顾正确性与对齐性。首先，我们提出了一套数学反馈评估准则，并证明GPT-4能有效利用该准则对人工撰写和LLM生成的反馈进行标注。其次，我们提出了一种基于强化学习优化正确性与对齐性的反馈生成框架。具体而言，我们利用GPT-4的标注结果对增强数据集中的反馈对创建偏好，并通过直接偏好优化进行训练。实验表明，该方法显著提升了开源LLM Llama 2生成反馈的正确性与对齐性；我们通过案例研究定性分析了生成与评估系统，并指出了未来工作的若干方向。