Direct Preference Optimization (DPO) has become an important method for aligning large language models (LLMs) with human preferences because it removes the need for explicit reward modeling and reinforcement learning. However, its performance depends heavily on the quality of preference data, and noisy preference data in real-world settings can weaken alignment performance. To address this issue, we propose a bilevel optimization framework and prove, under some idealized conditions, that this framework can recover the DPO optimum under clean data. We further derive a prior form for the learnable weighting function under label-flipping noise. Considering that high-quality metadata may be difficult to obtain, we propose a prompt augmentation consistency method that enables meta-learning even when metadata is completely unavailable. To reduce the high cost of higher-order gradients in LLM meta-learning, we combine central-difference approximation with LoRA fine-tuning and develop a scalable training scheme. Experiments on TL;DR summarization and Anthropic Helpful and Harmless dialogue show that the proposed method improves alignment performance over multiple DPO baselines under different noise rates.
This paper proposes a Linear Programming (LP)-based local search framework for fine-tuning pretrained transformer models with explicit control against overfitting. The approach formulates transformer fine-tuning as a bilevel optimization-based regularization problem, in which model parameters and regularization hyperparameters are jointly updated. Information collected during initial warm-up iterations, including validation gradients and training Hessian information, is used to construct a local descent direction by solving an LP that minimizes a scaled directional derivative while preserving training optimality. This validation-aware descent direction enables focused local updates of both parameters and regularization hyperparameters, reducing overfitting without requiring repeated full retraining cycles. The resulting method, termed Linear Programming-based Fine-Tuning (LiFT) for transformers, differs from conventional fine-tuning by systematically identifying task-specific updates rather than relying on heuristic or grid-based hyperparameter selection. Experiments on GPT-2 Small fine-tuned on WikiText-2 demonstrate that LiFT enables effective adaptation through selective tuning of transformer blocks and regularization parameters, yielding consistent improvements in test perplexity across multiple layer configurations and regularization settings, with particularly pronounced gains in overfitting-prone scenarios. Beyond empirical performance, LiFT establishes a principled connection between transformer fine-tuning, bilevel optimization, local search, and regularization theory.