VPO: Reasoning Preferences Optimization Based on $\mathcal{V}$-Usable Information

Direct Preference Optimization (DPO) is a widely used preference optimization algorithm in large language model (LLM) alignment, which reparameterizes the reward function in reinforcement learning with human feedback (RLHF) without requiring a separate reward model. However, during the DPO training process, when a large negative gradient is applied to low-confidence samples, LLMs with a softmax output head tend to squeeze the confidence in the model's output distribution towards the highest-confidence sentence, which may lead to a decrease in the confidence of both preference and non-preference samples, while increasing the confidence of unrelated tokens. This phenomenon becomes more complex in reasoning tasks. In this work, focusing on reasoning tasks, we propose VPO, a negative gradient constraint method for human non-preference samples based on $\mathcal{V}$-usable information. By using $\mathcal{V}$-usable information to measure the similarity between preference pairs and selectively constrain the negative gradient, VPO can alleviate the squeezing effect of DPO, enhance alignment with the generation objective, and maintain the model's ability to distinguish between preference and non-preference samples. We compare VPO with DPO and its latest variants on mathematical reasoning tasks using the LLama 3.1 and Qwen 2.5 series, including both Base and Instruct models. Our results demonstrate that VPO consistently and significantly outperforms existing methods. Specifically, on Qwen2.5-7B-Base, VPO achieves 7.80\% and 13.25\% improvement over DPO on MATH500 and AMC23, respectively. We also conduct ablation experiments and in-depth analysis on VPO to explain its effectiveness and rationale.