A Principled Loss Function for Direct Language Model Alignment

The alignment of large language models (LLMs) with human preferences is commonly achieved through Reinforcement Learning from Human Feedback (RLHF). Direct Preference Optimization (DPO) simplified this paradigm by establishing a direct mapping between the optimal policy and a reward function, eliminating the need for an explicit reward model. However, we argue that the DPO loss function is theoretically misaligned with its own derivation, as it promotes the indefinite maximization of a logits difference, which can lead to training instability and reward hacking. In this paper, we propose a novel loss function derived directly from the RLHF optimality condition. Our proposed loss targets a specific, finite value for the logits difference, which is dictated by the underlying reward, rather than its maximization. We provide a theoretical analysis, including a gradient-based comparison, to demonstrate that our method avoids the large gradients that plague DPO when the probability of dispreferred responses approaches zero. This inherent stability prevents reward hacking and leads to more effective alignment. We validate our approach by fine-tuning a Qwen2.5-7B model, showing significant win-rate improvements over a standard DPO baseline and achieving competitive performance against larger models like Llama-3.1-8B.