不用训练，仅调提示就能让大模型变好家教。
LLMs Are Already Good Tutors: Training-Free Prompt Optimization for Pedagogical Math Tutoring
- 用12种提示优化方法，只改系统提示不训练模型。
- 最佳方法在解题率、防泄露、帮助性上综合表现超强化学习模型。
- 适合想快速部署教育AI、算力有限的研究者或开发者。
将大语言模型对齐用于数学辅导通常需要基于强化学习的训练及多GPU资源。本文探究仅通过API调用演化系统提示（训练-free提示优化）是否可作为实用替代方案。我们复现了7种已有方法，并提出5种教育专用方法，在两个分布外基准测试集上于5种条件下评估这12种方法。所有最佳配置均超越最强的强化学习训练基线（R_total = 0.633），其中ParetoGrad在后测解题率、泄漏控制与助人度之间取得最优帕累托平衡，而非单一指标领先。行为分析使用82项教育代码本发现，训练-free方法依赖教学知识模式的频率是强化学习模型的2-3倍，但意图级支架支持低约10个百分点。还观察到任务依赖的推理模式效应，在训练-free与强化学习范式中均一致。该方法仅靠提示即可高效实现具有教学对齐能力的LLM导师，且计算开销极小。
原文摘要 · Abstract (English)
Aligning LLMs for math tutoring typically requires RL-based training with multi-GPU infrastructure. We investigate whether training-free prompt optimization-evolving only the system prompt via API calls-can serve as a practical alternative. We adapt 7 published methods and propose 5 education-specialized methods, evaluating these 12 methods under 5 conditions on 2 OOD benchmark suites. All 12 best-per-method configurations surpass the strongest RL-trained baseline (R_total = 0.633), and our ParetoGrad achieves the best Pareto balance across post-test solve rate, leak control, and helpfulness, rather than dominating any single component. Behavioral analysis with an 82-code educational codebook reveals that training-free methods rely on teaching-knowledge patterns at 2-3x the rate of RL-trained models, with a compensating ~10 percentage-point reduction in intent-level scaffolding. We also find a task-dependent reasoning mode effect consistent across training-free and RL-based paradigms. Our approach enables efficient development of pedagogically aligned LLM tutors with prompts alone and minimal compute.
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