用预训练+微调解决小数据大决策问题,提升模型泛化能力。
LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimization
- 基于领域知识生成合成数据预训练,再用真实数据微调。
- 在少量真实数据下实现高精度决策,且实例越多效果越佳。
- 适合资源有限但需大规模决策的工业场景,如供应链优化。
我们研究小数据、大规模决策问题:企业需同时对大量产品做出运营决策,但每项决策仅能观测到少量、可能含噪的数据。受大语言模型成功启发,我们提出一种基于定制Transformer的预训练-微调方法。模型首先在包含管理知识和决策环境结构特征的大规模合成数据上预训练,随后在真实观测数据上微调。该流程兼具双重优势:预训练注入领域知识,使高容量模型可借助丰富合成数据训练;微调则使模型适配实际操作环境,提升与真实数据生成机制的一致性。尽管采用Transformer的注意力机制以高效提取跨任务结构,但方法并非现成套用,而是依赖问题特定的架构设计和定制化训练流程。理论上,我们首次建立针对此类情境下Transformer学习的全面误差分析,给出非渐近保证,验证方法有效性。关键发现是预训练与微调共同决定性能,主导因素取决于两者中更优者;尤其微调呈现规模经济效应——随着实例数量增加,迁移学习效果持续提升。
原文摘要 · Abstract (English)
We consider small-data, large-scale decision problems in which a firm must make many operational decisions simultaneously (e.g., across a large product portfolio) while observing only a few, potentially noisy, data points per instance. Inspired by the success of large language models (LLMs), we propose a pretrain-then-finetune approach built on a designed Transformer model to address this challenge. The model is first pretrained on large-scale, domain-informed synthetic data that encode managerial knowledge and structural features of the decision environment, and is then fine-tuned on real observations. This new pipeline offers two complementary advantages: pretraining injects domain knowledge into the learning process and enables the training of high-capacity models using abundant synthetic data, while finetuning adapts the pretrained model to the operational environment and improves alignment with the true data-generating regime. While we have leveraged the Transformer's state-of-the-art representational capacity, particularly its attention mechanism, to efficiently extract cross-task structure, our approach is not an off-the-shelf application. Instead, it relies on problem-specific architectural design and a tailored training procedure to match the decision setting. Theoretically, we develop the first comprehensive error analysis regarding Transformer learning in relevant contexts, establishing nonasymptotic guarantees that validate the method's effectiveness. Critically, our analysis reveals how pretraining and fine-tuning jointly determine performance, with the dominant contribution governed by whichever is more favorable. In particular, finetuning exhibits an economies-of-scale effect, whereby transfer learning becomes increasingly effective as the number of instances grows.
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