Permutative Preference Alignment from Listwise Ranking of Human Judgments

Aligning Large Language Models (LLMs) with human preferences is crucial in ensuring desirable and controllable model behaviors. Current methods, such as Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO), rely on the Bradley-Terry (B-T) model to maximize the likelihood of pairwise choices. However, when multiple responses are available, the B-T model fails to guarantee an accurate list ranking of the responses. To address this issue, we propose Permutative Preference Alignment (PPA), a novel offline listwise approach that incorporates the Normalized Discounted Cumulative Gain (NDCG), a widely-used ranking metric, as an alternative training objective for LLM alignment. We develop an end-to-end alignment algorithm by approximating NDCG with a differentiable surrogate loss. Experiments demonstrate that PPA outperforms existing pairwise and listwise methods on evaluation sets and general benchmarks such as AlpacaEval. Furthermore, we show that NDCG-based approaches improve ranking accuracy more effectively than B-T-based methods and provide a theoretical explanation for this improvement.