Full-Step-DPO: Self-Supervised Preference Optimization with Step-wise Rewards for Mathematical Reasoning

• URL: http://arxiv.org/abs/2502.14356v1
• Date: Thu, 20 Feb 2025 08:28:11 GMT
• Title: Full-Step-DPO: Self-Supervised Preference Optimization with Step-wise Rewards for Mathematical Reasoning
• Authors: Huimin Xu, Xin Mao, Feng-Lin Li, Xiaobao Wu, Wang Chen, Wei Zhang, Anh Tuan Luu,
• Abstract summary: We propose Full-Step-DPO, a novel DPO framework tailored for mathematical reasoning. Instead of optimizing only the first erroneous step, it leverages step-wise rewards from the entire reasoning chain. We show that Full-Step-DPO achieves superior performance compared to state-of-the-art baselines.
• Score: 30.096211889103998
• License:
• Abstract: Direct Preference Optimization (DPO) often struggles with long-chain mathematical reasoning. Existing approaches, such as Step-DPO, typically improve this by focusing on the first erroneous step in the reasoning chain. However, they overlook all other steps and rely heavily on humans or GPT-4 to identify erroneous steps. To address these issues, we propose Full-Step-DPO, a novel DPO framework tailored for mathematical reasoning. Instead of optimizing only the first erroneous step, it leverages step-wise rewards from the entire reasoning chain. This is achieved by training a self-supervised process reward model, which automatically scores each step, providing rewards while avoiding reliance on external signals. Furthermore, we introduce a novel step-wise DPO loss, which dynamically updates gradients based on these step-wise rewards. This endows stronger reasoning capabilities to language models. Extensive evaluations on both in-domain and out-of-domain mathematical reasoning benchmarks across various base language models, demonstrate that Full-Step-DPO achieves superior performance compared to state-of-the-art baselines.

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