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

TL;DR

This paper introduces SPPD, a novel self-training framework that uses process preference learning with dynamic value margins, improving reasoning capabilities of large language models without relying on distillation or human annotations.

Contribution

The paper proposes SPPD, a self-training method utilizing process-based MDP and dynamic value margins, theoretically linking it to policy gradient methods and demonstrating superior performance.

Findings

Outperforms existing methods on mathematical benchmarks

Eliminates need for distillation or human annotations

Proves theoretical equivalence to policy gradient methods

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}.