Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shift. 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 which measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates that CIL learns features that satisfy the invariant constraint with infinite samples. 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.

Typical machine learning applications always assume the data follows independent and identically distributed (IID) assumptions. In contrast, this assumption is frequently violated in real-world circumstances, leading to the Out-of-Distribution (OOD) generalization problem and a major drop in model robustness. To mitigate this issue, the invariant learning technique is leveraged to distinguish between spurious features and invariant features among all input features and to train the model purely on the basis of the invariant features. Numerous invariant learning strategies imply that the training data should contain domain information. Such information includes the environment index or auxiliary information acquired from prior knowledge. However, acquiring these information is typically impossible in practice. In this study, we present TIVA for environment-independent invariance learning, which requires no environment-specific information in training data. We discover and prove that, given certain mild data conditions, it is possible to train an environment partitioning policy based on attributes that are independent of the targets and then conduct invariant risk minimization. We examine our method in comparison to other baseline methods, which demonstrate superior performance and excellent robustness under OOD, using multiple benchmarks.

Offline goal-conditioned RL (GCRL) offers a way to train general-purpose agents from fully offline datasets. In addition to being conservative within the dataset, the generalization ability to achieve unseen goals is another fundamental challenge for offline GCRL. However, to the best of our knowledge, this problem has not been well studied yet. In this paper, we study out-of-distribution (OOD) generalization of offline GCRL both theoretically and empirically to identify factors that are important. In a number of experiments, we observe that weighted imitation learning enjoys better generalization than pessimism-based offline RL method. Based on this insight, we derive a theory for OOD generalization, which characterizes several important design choices. We then propose a new offline GCRL method, Generalizable Offline goAl-condiTioned RL (GOAT), by combining the findings from our theoretical and empirical studies. On a new benchmark containing 9 independent identically distributed (IID) tasks and 17 OOD tasks, GOAT outperforms current state-of-the-art methods by a large margin.