Dual-Difficulty Curriculum Learning for Direct Preference Optimization

Preference optimization is widely used to align Large Language Models (LLMs) with preference feedback. However, most existing methods train on a single positive-negative pair per prompt, discarding additional supervision available in preference datasets that typically contain multiple candidate responses. Motivated by this limitation, recent work explores group-wise preference optimization, which jointly contrasts multiple responses for the same prompt, but its empirical behavior and scalability remain underexplored due to the memory overhead of group-coupled objectives. In this work, we present a unified empirical and systems study of group-wise preference optimization and develop a memory-efficient implementation for group-coupled objectives. By instantiating first-order linearization with objective-specific per-response coefficients, our implementation preserves first-order gradients while decoupling samples during backpropagation, substantially reducing peak memory usage and enabling scalable training with larger groups. Across offline and online settings, we show that leveraging multiple responses consistently outperforms single-pair training. Furthermore, incorporating a negative log-likelihood (NLL) term on positive responses is critical for both performance gains and training stability.

Fine-tuning large language models (LLMs) to align with human preferences has driven the success of systems such as Gemini and ChatGPT. However, approaches like Reinforcement Learning from Human Feedback (RLHF) remain computationally expensive and complex. Direct Preference Optimization (DPO) offers a simpler alternative but has limitations such as inconsistent ranking accuracy, high dependence on GPU resources, and expensive hyperparameter tuning. We propose the Convex Optimization for Alignment and Preference Learning Algorithm (COALA): a novel lightweight strategy with strong theoretical guarantees. By leveraging the convex optimization reformulation of neural networks, COALA eliminates the need for a reference model and obtains significant reduction in both training time and VRAM consumption, thus enabling efficient training on a single GPU. Experiments across four datasets--including a 26621-sample synthetic Educational Feedback dataset--and six models (including Llama-3.1-8B) demonstrate COALA's competitive performance and efficiency while utilizing as little as ~17.6% of DPO's total TFLOPs. COALA exhibits stable, monotonically increasing rewards and reaches peak margins in significantly shorter time in comparison to traditional methods such as DPO and ORPO. To the best of our knowledge, this is the first time convex optimization has been effectively applied to preference fine-tuning of LLMs.

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.