Recent research has attempted to associate preference optimization (PO) performance with the underlying preference datasets. In this work, our observation is that the differences between the preferred response $y^+$ and dispreferred response $y^-$ influence what LLMs can learn, which may not match the desirable differences to learn. Therefore, we use distance and reward margin to quantify these differences, and combine them to get Distance Calibrated Reward Margin (DCRM), a metric that measures the quality of a response pair for PO. Intuitively, DCRM encourages minimal noisy differences and maximal desired differences. With this, we study 3 types of commonly used preference datasets, classified along two axes: the source of the responses and the preference labeling function. We establish a general correlation between higher DCRM of the training set and better learning outcome. Inspired by this, we propose a best-of-$N^2$ pairing method that selects response pairs with the highest DCRM. Empirically, in various settings, our method produces training datasets that can further improve models' performance on AlpacaEval, MT-Bench, and Arena-Hard over the existing training sets.

Offline preference optimization offers a simpler and more stable alternative to RLHF for aligning language models. However, their effectiveness is critically dependent on ranking accuracy, a metric where further gains are highly im-pactful. This limitation arises from a fundamental problem that we identify and formalize as the Overfitting-Underfitting Dilemma: current margin designs cause models to apply excessive, wasteful gradients to correctly ranked samples (over-fitting) while providing insufficient corrective signals for misranked ones (underfitting). To resolve this dilemma, we propose Adaptive Margin-attached Preference Optimization (AMaPO), a simple yet principled algorithm. AMaPO employs an instance-wise adaptive margin, refined by Z-normalization and exponential scaling, which dynamically reallocates learning effort by amplifying gradients for mis-ranked samples and suppressing them for correct ones. Extensive experiments on widely used benchmarks demonstrate that AMaPO not only achieves better ranking accuracy and superior downstream alignment performance, but targeted analysis also confirms that it successfully mitigates the core overfitting and underfitting issues.

The alignment of Large Language Models (LLMs) is crucial for ensuring their safety and reliability in practical applications. Direct Preference Optimization (DPO) has emerged as an efficient method that directly optimizes models using preference pairs, significantly reducing resource demands. However, the effectiveness of DPO heavily depends on the data quality, which is frequently compromised by noise. In this work, we propose $γ$-PO, a dynamic target margin preference optimization algorithm that adjust reward margins at the pairwise level. By introducing instance-specific margin calibration, $γ$-PO strategically prioritizes high-confidence pairs (those demonstrating higher reward margins) while suppressing potential noise from ambiguous pairs. Moreover, $γ$-PO is a plug-and-play method, compatible with variants of DPO that rely on reward margin between preference pairs. Across benchmarks such as AlpacaEval2 and Arena-Hard, $γ$-PO achieves an average 4.4\% improvement over other baselines, setting new benchmarks for state-of-the-art performance. Additionally, $γ$-PO requires minimal code changes and has a negligible impact on training efficiency, making it a robust solution for enhancing LLMs alignment. Our codes are available at \href{https://github.com/sunjie279/gammaPO}{https://github.com/sunjie279/gammaPO}.

Additionally, we introduce a target reward margin to the Bradley-Terry objective to encourage a larger margin between the winning and losing responses, further improving the algorithm's performance.

Direct Preference Optimization (DPO) has emerged as a simple and effective method for aligning large language models. However, its reliance on a fixed temperature parameter leads to suboptimal training on diverse preference data, causing overfitting on easy examples and under-learning from informative ones. Recent methods have emerged to counter this. While IPO addresses general overfitting, its uniform regularization can be overly conservative. The more targeted approach of $β$-DPO suffers from its own limitations: its batch-level adaptation applies a single, compromised temperature to mixed-margin pairs, its linear update rule can produce unstable negative $β$ values, and its filtering mechanism discards potentially useful training signals. In this work, we introduce Margin-Adaptive Direct Preference Optimization (MADPO), a method that provides a stable, data-preserving, and instance-level solution. MADPO employs a practical two-step approach: it first trains a reward model to estimate preference margins and then uses these margins to apply a continuous, adaptive weight to the DPO loss for each individual training sample. This re-weighting scheme creates an effective target margin that is amplified for hard pairs and dampened for easy pairs, allowing for granular control over the learning signal. We provide a comprehensive theoretical analysis, proving that MADPO has a well-behaved optimization landscape and is robust to reward model estimation errors. We validate our theory with experiments on a sentiment generation task, where MADPO consistently and significantly outperforms strong baselines across datasets of varying quality. It achieves performance gains of up to +33.3\% on High Quality data and +10.5\% on Low Quality data over the next-best method. Our results establish MADPO as a more robust and principled approach to preference alignment.

Direct Preference Optimization (DPO) have emerged as a popular method for aligning Large Language Models (LLMs) with human preferences. While DPO effectively preserves the relative ordering between chosen and rejected responses through pairwise ranking losses, it often neglects absolute reward magnitudes. This oversight can decrease the likelihood of chosen responses and increase the risk of generating out-of-distribution responses, leading to poor performance. We term this issue Degraded Chosen Responses (DCR).To address this issue, we propose Balanced Preference Optimization (BPO), a novel framework that dynamically balances the optimization of chosen and rejected responses through two key components: balanced reward margin and gap adaptor. Unlike previous methods, BPO can fundamentally resolve DPO's DCR issue, without introducing additional constraints to the loss function. Experimental results on multiple mathematical reasoning tasks show that BPO significantly outperforms DPO, improving accuracy by +10.1% with Llama-3.1-8B-Instruct (18.8% to 28.9%) and +11.7% with Qwen2.5-Math-7B (35.0% to 46.7%). It also surpasses DPO variants by +3.6% over IPO (43.1%), +5.0% over SLiC (41.7%), and +3.1% over Cal-DPO (43.6%) on the same model. Remarkably, our algorithm requires only a single line of code modification, making it simple to implement and fully compatible with existing DPO-based frameworks.

Aligning large language models (LLMs) with human preferences is critical for real-world deployment, yet existing methods like RLHF face computational and stability challenges. While DPO establishes an offline paradigm with single hyperparameter $\beta$, subsequent methods like SimPO reintroduce complexity through dual parameters ($\beta$, $\gamma$). We propose {ReLU-based Preference Optimization (RePO)}, a streamlined algorithm that eliminates $\beta$ via two advances: (1) retaining SimPO's reference-free margins but removing $\beta$ through gradient analysis, and (2) adopting a ReLU-based max-margin loss that naturally filters trivial pairs. Theoretically, RePO is characterized as SimPO's limiting case ($\beta \to \infty$), where the logistic weighting collapses to binary thresholding, forming a convex envelope of the 0-1 loss. Empirical results on AlpacaEval 2 and Arena-Hard show that RePO outperforms DPO and SimPO across multiple base models, requiring only one hyperparameter to tune.

Preference learning is critical for aligning large language models (LLMs) with human values, with the quality of preference datasets playing a crucial role in this process. While existing metrics primarily assess data quality based on either explicit or implicit reward margins, they often provide contradictory evaluations for the same data. To address this issue, we introduce the alignment potential metric, which quantifies the gap from the model's current implicit reward margin to the target explicit reward margin, thereby estimating the model's potential to align with the preference data. Empirical results demonstrate that training on data selected by this metric consistently enhances alignment performance, surpassing existing metrics across different base models and optimization objectives. Furthermore, our method extends to self-play data generation frameworks, where the metric is used to identify high-quality data within the self-generated content by LLMs. Under this data generation scenario, our method surpasses current state-of-the-art (SOTA) results across various training settings and demonstrates continuous improvements in alignment performance as dataset size and training iterations increase.

Direct Preference Optimization (DPO) has emerged as a promising approach for aligning large language models with human preferences. While prior work mainly extends DPO from the aspect of the objective function, we instead improve DPO from the largely overlooked but critical aspect of data selection. Specifically, we address the issue of parameter shrinkage caused by noisy data by proposing a novel margin-maximization principle for dataset curation in DPO training. To accurately estimate margins for data selection, we propose a dual-margin guided approach that considers both external reward margins and implicit DPO reward margins. Extensive experiments demonstrate that our method reduces computational cost dramatically while improving performance. Remarkably, by using just 10\% of the Ultrafeedback dataset, our approach achieves 3\% to 8\% improvements across various Llama and Mistral series models on the AlpacaEval 2.0 benchmark. Furthermore, our approach seamlessly extends to iterative DPO, yielding a roughly 3\% improvement with 25\% online data, while further reducing training time. These results highlight the potential of data selection strategies for advancing preference optimization.