Small large language models (LLMs) often face difficulties in aligning output to human preferences, particularly when operating under severe performance gaps. In this work, we propose two lightweight DPO-based variants -- Adaptive Margin-Sigmoid Loss and APO-hinge-zero -- to better address underperformance scenarios by introducing margin-based objectives and selective update mechanisms. Our APO-hinge-zero method, which combines hinge-induced hard-example mining with the chosen-focused optimization of APO-zero, achieves strong results. In AlpacaEval, APO-hinge-zero improves the win rate by +2.0 points and the length-controlled win rate by +1.4 points compared to the APO-zero baseline. In MT-Bench, our methods maintain competitive performance in diverse categories, particularly excelling in STEM and Humanities tasks. These results demonstrate that simple modifications to preference-based objectives can significantly enhance small LLM alignment under resource constraints, offering a practical path toward more efficient deployment.
@article{arxiv.2508.08466,
title = {Enhancing Small LLM Alignment through Margin-Based Objective Modifications under Resource Constraints},
author = {Daren Yao and Jinsong Yuan and Ruike Chen},
journal= {arXiv preprint arXiv:2508.08466},
year = {2025}
}