Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

翻译：不变性学习方法旨在学习不变特征，以期在分布偏移下实现泛化。尽管许多任务天然具有连续域特征，但当前的不变性学习技术通常假设域索引为分类变量。例如，云计算中的自动扩缩容常需要跨不同时间（如一天中的时刻、一年中的日期）泛化的CPU利用率预测模型，其中"时间"是连续域索引。本文首先从理论上证明现有不变性学习方法可能无法解决连续域问题。具体而言，将连续域分割为离散域的朴素解法忽视了域间的内在联系，因此可能导致次优性能。为解决这一挑战，我们提出连续不变性学习（CIL），该方法可提取跨连续索引域的不变特征。CIL是一种创新的对抗性流程，能够衡量并控制标签与连续域索引在给定提取特征条件下的条件独立性。理论分析证明了CIL相较于现有不变性学习方法的优越性。在合成数据集与真实世界数据集（包括从生产系统采集的数据）上的实验结果表明，CIL在所有任务中均持续优于强基线方法。