Mind the Gap: Structure-Aware Consistency in Preference Learning

Direct Preference Optimization (DPO) has emerged as a popular alternative to Reinforcement Learning from Human Feedback (RLHF), offering theoretical equivalence with simpler implementation. We prove this equivalence is conditional rather than universal, depending on an implicit assumption frequently violated in practice: the RLHF-optimal policy must prefer human-preferred responses. When this assumption fails, DPO optimizes relative advantage over the reference policy rather than absolute alignment with human preferences, leading to pathological convergence where policies decrease DPO loss while preferring dispreferred responses. We characterize when this assumption is violated, show the existence of an undesirable solution space, and prove that DPO and RLHF optimize fundamentally different objectives in such cases. To address this, we introduce Constrained Preference Optimization (CPO), augmenting RLHF with constraints for provable alignment. We further provide a geometric interpretation through soft margin ranking, revealing that DPO implements margin ranking with potentially negative targets. Our theoretical analysis establishes when DPOs' guarantees hold and provides solutions preserving simplicity with provable alignment. Comprehensive experiments on standard benchmarks demonstrate that CPO achieves state-of-the-art performance. Code is available at: https://github.com/visitworld123/CPO.

Although Large Language Models (LLMs) have made remarkable progress, current preference optimization methods still struggle to align directional consistency while preserving reasoning diversity. To address this limitation, we propose Directional-Groupwise Preference Optimization (DGPO), a lightweight framework that aggregates supervision signals at the group level and explicitly models direction-aware alignment through multi-candidate comparisons. DGPO organizes forward and reverse question-answer instances into structured sets and optimizes a margin-based likelihood objective that separates coherent reasoning paths from inconsistent alternatives. This group-wise formulation captures richer relative information than pairwise objectives and reinforces consistency across diverse reasoning pathways. Empirical results show that our constructed reverse data yields a 3.2% average improvement across five benchmarks, while DGPO further delivers consistent gains across multiple datasets and model families, achieving average accuracy improvements of up to 3.6%.

Curriculum learning enhances Direct Preference Optimization (DPO) for aligning Large Language Models (LLMs), yet existing methods rely on a one-dimensional view of difficulty. In this work, we reframe alignment difficulty as a two-dimensional space spanned by Prompt Complexity (PC) and Pairwise Distinguishability (PD), providing a more principled foundation for alignment. We first demonstrate the efficacy of this space by developing DM-Curri-DPO, a framework of static curricula that already achieves significant gains over baseline methods. Moving beyond these handcrafted paths, we introduce our primary contribution: GSP-Curri-DPO, a novel Group-wise Self-Paced Learning framework. This advanced method empowers the model to navigate the difficulty grid, discovering an optimal learning trajectory based on its own evolving capabilities. Extensive experiments show our self-paced approach not only sets a new state-of-the-art on key benchmarks but, more importantly, demonstrates superior data efficiency and robustness to preference noise. Our work establishes a new paradigm for LLM alignment, offering both a structured difficulty space and an intelligent, model-driven methodology for navigating it.