SPPD: Self-training with Process Preference Learning Using Dynamic Value Margin

• URL: http://arxiv.org/abs/2502.13516v1
• Date: Wed, 19 Feb 2025 08:11:26 GMT
• Title: SPPD: Self-training with Process Preference Learning Using Dynamic Value Margin
• Authors: Hao Yi, Qingyang Li, Yulan Hu, Fuzheng Zhang, Di Zhang, Yong Liu,
• Abstract summary: We propose textbfSelf-training framework integrating textbfProcess textbfPreference learning using textbfDynamic value margin (SPPD)<n>Experiments on 7B-scale models demonstrate superior performance across in-domain and out-domain mathematical benchmarks.
• Score: 16.346540681903804
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, enhancing the numerical and logical reasoning capability of Large Language Models (LLMs) has emerged as a research hotspot. Existing methods face several limitations: inference-phase techniques (e.g., Chain of Thoughts) rely on prompt selection and the pretrained knowledge; sentence-level Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO) struggle with step-wise mathematical correctness and depend on stronger models distillation or human annotations; while Reinforcement Learning (RL) approaches incur high GPU memory costs and unstable training. To address these, we propose \textbf{S}elf-training framework integrating \textbf{P}rocess \textbf{P}reference learning using \textbf{D}ynamic value margin (SPPD). SPPD leverages a process-based Markov Decision Process (MDP) and Bellman optimality equation to derive \textbf{dynamic value margin} on step-level preference optimization, which employs tree-based self-sampling on model responses \textbf{without any distillation} from other models. Furthermore, we theoretically prove that SPPD is \textbf{equivalent to on-policy policy gradient methods} under reward constraints. Experiments on 7B-scale models demonstrate superior performance across in-domain and out-domain mathematical benchmarks. We open-source our code at \href{https://anonymous.4open.science/r/SSDPO-D-DCDD}{https://anonymous.4open.science/r/SPPD-DCDD}.

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