Relative Density Ratio Optimization for Stable and Statistically Consistent Model Alignment

Preference-based alignment methods such as Direct Preference Optimization (DPO) use pairwise preferences labeled by human annotators to fine-tune language models. However, annotators carry systematic biases toward some attributes: a name that signals a gender or an ethnicity, a persona, a language variety, a formatting convention, or length. If not properly addressed, these systematic biases can be absorbed and amplified during alignment. Existing methods address length bias or annotator disagreement, but fail to eliminate biases toward arbitrary attributes. To address this limitation, we propose Bias-Adjusted DPO (BA-DPO), a generalization of DPO that adds one bias parameter per annotator toward responses carrying a declared attribute. We prove that the objective is convex in the bias parameters and that the votes identify each annotator's bias up to a shared constant. The remaining constant is what fixes the aligned model's attribute rate: by default the rate of the reference model, or a target rate, which we use to bring a biased policy to statistical parity. On a corpus with planted biases, DPO drives the attribute from a balanced start to probability 0.96 and BA-DPO removes 81 to 95% of that shift; on MultiPref with real annotators it removes about half of DPO's lengthening. Both hold at 0.5B with full fine-tuning and at 8B with LoRA, at no higher KL than DPO and no loss in judged quality.

Alignment of large language models typically relies on pairwise preference feedback, though ranked feedback can capture more comprehensive information across multiple responses within a single annotation. However, ranked-preference alignment is underexplored in practice compared to simpler pairwise approaches, potentially resulting in suboptimal behavior. Concurrently, recent research has conceptualized large language model alignment objectives as divergence estimators between aligned (preferred) and unaligned (less-preferred) response distributions, resulting in a family of objectives with an interpretable theoretical foundation and strong empirical performance. This work unifies these perspectives by introducing $f$-RPO, a $f$-divergence objective for ranked preference optimization that extends divergence-based alignment to ranked feedback and recovers pairwise preference alignment as a special case. Our theoretical analysis establishes rank-order consistency, showing that $f$-RPO preserves the underlying preference ordering at convergence. Empirical results indicate that total-variation and reverse-KL variants of the proposed objective consistently outperform ranked-alignment baselines in both ranking and generation quality across Qwen, Llama, & Gemma models ranging from 0.5B to 8B parameters.

The alignment of large language models with human preferences is commonly achieved through Reinforcement Learning from Human Feedback or Direct Preference Optimization. However, these methods are vulnerable to the significant noise prevalent in real-world preference datasets. To address this critical issue, we present a theoretical framework for unbiased alignment, introducing the Unbiased Reward Model (URM) loss and the Unbiased Direct Preference Optimization (UDPO) loss. By mathematically correcting the distortion induced by preference noise, our novel objectives enable unbiased model training directly from noisy datasets, without requiring clean ground-truth supervision. We provide rigorous theoretical analyses demonstrating that our methods are noise-tolerant, parameter downward compatible, and classification-calibrated. Comprehensive experiments across diverse datasets demonstrate that our approaches outperform state-of-the-art baselines. Code available at: https://github.com/cswjl/unbiased-alignment.