Self-Training with Direct Preference Optimization Improves Chain-of-Thought Reasoning
This work addresses the need for scalable and stable training methods for small language models in mathematical reasoning tasks, though it is incremental as it builds on existing self-training and preference learning techniques.
The paper tackles the problem of training language models for mathematical reasoning by proposing a self-training method enhanced with Direct Preference Optimization, which improves reasoning performance and offers a more cost-effective solution compared to using large proprietary models.
Effective training of language models (LMs) for mathematical reasoning tasks demands high-quality supervised fine-tuning data. Besides obtaining annotations from human experts, a common alternative is sampling from larger and more powerful LMs. However, this knowledge distillation approach can be costly and unstable, particularly when relying on closed-source, proprietary LMs like GPT-4, whose behaviors are often unpredictable. In this work, we demonstrate that the reasoning abilities of small-scale LMs can be enhanced through self-training, a process where models learn from their own outputs. We also show that the conventional self-training can be further augmented by a preference learning algorithm called Direct Preference Optimization (DPO). By integrating DPO into self-training, we leverage preference data to guide LMs towards more accurate and diverse chain-of-thought reasoning. We evaluate our method across various mathematical reasoning tasks using different base models. Our experiments show that this approach not only improves LMs' reasoning performance but also offers a more cost-effective and scalable solution compared to relying on large proprietary LMs.