Do Post-Training Algorithms Actually Differ? A Controlled Study Across Model Scales Uncovers Scale-Dependent Ranking Inversions

Direct preference optimisation (DPO) is widely used for language model post-training, but its performance depends strongly on the choice of its hyperparameters, such as the learning rate and the reference-policy regularisation parameter $β$. To better understand the DPO hyperparameter landscape, we conduct extensive experiments using a dense hyperparameter grid across different model scales from the same family. This allows us to analyse how the optimal DPO hyperparameters evolve with model size and the number of update steps, with intermediate checkpoints providing an inexpensive signal to accelerate the hyperparameter optimisation process. Furthermore, by evaluating our models on both static and dynamic benchmarks, we identify which benchmarks provide the strongest signal for hyperparameter selection. Finally, we investigate how different state-of-the-art hyperparameter optimisation strategies perform in this setting. Our experiments show that the optimal learning rate varies with model size and that hyperparameters are not transferable across training datasets. We also find that validation loss is a poor proxy for hyperparameter optimisation, as hyperparameters that minimize validation loss only weakly correlate with optimal hyperparameters for downstream benchmarks. Therefore, DPO hyperparameters need to be tuned specifically for the target model, dataset, and evaluation objective. We also show that short candidate training runs can substantially reduce the cost of this selection. We release all our training configurations and evaluation results to support reproducible analysis of selection quality and training cost.

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.