Evolving Replay Hulls for Geometrically Supported Continual Domain Shift Learning

Unsupervised continual domain shift learning (UCDSL) requires continual adaptation to sequentially arriving unlabeled domains while retaining previously acquired knowledge and generalizing to future domains. However, its reliance on self-training makes continual adaptation vulnerable to unreliable pseudo-labels, whose errors can accumulate across domain stages. We propose a reliable UCDSL framework that estimates pseudo-label confidence from class-wise replay geometry. Replay samples of each class define a convex hull in representation space, and target reliability is measured by relative distances to class-wise hulls. The framework maintains informative replay regions throughout continual adaptation, allowing this confidence criterion to remain effective as new domains are encountered. We theoretically show how the coverage of class-wise replay hulls and sample distances to them relate to classification risk on unseen domains. Empirically, the proposed framework improves adaptation, generalization, and forgetting alleviation across multiple benchmark datasets, while achieving better predictive calibration than existing UCDSL methods.