Organizations: 1The Hong Kong University of Science and Technology · 2LIGHTSPEED · 3Hong Kong Baptist University.
Abstract
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.
DPO has become a widely adopted alternative to RLHF for aligning LLMs with human preferences, eliminating the need for a separate reward model or RL loop. Recent theoretical analysis uncovers an asymmetric gradient behavior in DPO: the loss suppresses dispreferred responses substantially faster than it promotes preferred ones, causing the model to learn to avoid bad answers rather than to generate good ones. We propose AdaDPO, a Self-Adaptive variant of the DPO algorithm that introduces per-preference-pair, stop-gradient-based coefficients derived directly from the policy model's generation probabilities, with the reference model's probabilities as an optional component. AdaDPO is constructed to enforce equality of gradient magnitudes between preferred and dispreferred probabilities; the practical implementation balances per-token gradients and applies a numerical clipping bound for stability, while retaining DPO's original hyperparameter structure. On Llama-3-8B-Instruct trained on UltraFeedback under a SimPO similar setup, AdaDPO consistently outperforms DPO on AlpacaEval 2: it achieves higher length-controlled win rates (LC) in 81% of hyperparameter combinations, attains the global best LC (48.3%) and raw win rate (46.1%), and enlarges the LC-over-WR margin in 88% of combinations, indicating effective mitigation of length bias. Additional analyses on KL divergence, reward margin, and reward accuracy confirm that AdaDPO rectifies the gradient imbalance and yields more efficient optimization. Because it operates purely at the loss level, AdaDPO can be dropped into existing preference-based alignment pipelines without changing data collection or model architectures. The method requires only a few lines of code, and the same self-adaptive principle generalizes to a broad family of pairwise contrastive preference losses including SimPO, R-DPO, IPO, CPO, and ORPO.
Offline preference optimization has become a practical substitute for reinforcement learning from human feedback, but pairwise objectives such as Direct Preference Optimization (DPO) and its variants use only the chosen and rejected responses stored in a static dataset. This leaves a useful signal unused: the response that the reference model itself would generate for the same prompt. We propose Direct Preference Optimization with Penalization (DPOP), a simple extension of DPO that augments the base preference loss with a gated penalty on reference-greedy responses. DPOP activates this penalty only when the current policy still assigns a lower likelihood to the preferred response than to the rejected response. On AlpacaEval 2.0, DPOP improves length-controlled win rate over DPO, SimPO, and AlphaDPO on both Llama-3-8b-it and Gemma-2-9b-it, achieving relative gains of 5.3% and 4.4% over baselines on the two models, respectively. Ablations further show that a SimNPO-style length-normalized penalty is stronger than NPO and token-level unlikelihood in this setting.
Preference-based reinforcement learning (RL) is a key paradigm for aligning policies with human judgments, yet its theoretical behavior in distributed settings where preference data are fragmented across heterogeneous users remains poorly understood. Direct Preference Optimization (DPO) avoids explicit reward modeling but lacks convergence guarantees under federated and decentralized training, where communication constraints and non-IID preferences fundamentally alter optimization dynamics. We provide the first convergence and time-complexity analysis of DPO in distributed environments. Modeling personalized offline RL with user-specific preference distributions, we characterize the induced global optimization landscape. For federated DPO, we derive convergence rates that quantify the impact of client drift, communication frequency, and preference heterogeneity; for decentralized DPO, we establish convergence over general communication graphs and show how spectral connectivity governs optimization speed and consensus. Empirically, we corroborate our theoretical insights on standard alignment benchmarks, demonstrating that our proposed methods not only enjoy strong theoretical guarantees but also deliver robust and scalable performance in practice. The code base is available here.