In this section, we show the proofs of the results in the main body. Eq. (1) satisfies the triangle inequality, i.e., for any scoring functions For the second inequality, we prove it similarly. Before we present the proof of the theorem, we first provide some lemmas. By applying Lemma A.2, the following holds with probability at least 1 α: null R F). Thus we have: null R A.1, we can get that the margin loss satisfies the triangle inequality. By Lemma A.4, we have R By Theorem 4.4, the following holds for any Based on Theorem A.6, the following standard error bound for gradual AST can be derived similarly to Corollary 4.6.

Empirically, the gradual self-training method greatly improves the target domain's accuracy compared

Concretely, we propose a coarse-to-fine framework, which starts with acoarsedomain discovery step via progressive domain discriminator training.

The effectiveness of unsupervised domain adaptation degrades when there is a large discrepancy between the source and target domains. Gradual domain adaption (GDA) is one promising way to mitigate such an issue, by leveraging additional unlabeled data that gradually shift from the source to the target. Through sequentially adapting the model along the indexed intermediate domains, GDA substantially improves the overall adaptation performance. In practice, however, the extra unlabeled data may not be separated into intermediate domains and indexed properly, limiting the applicability of GDA. In this paper, we investigate how to discover the sequence of intermediate domains when it is not already available.

In this paper, we propose a new method called Self-Training with Dynamic Weighting (STDW), which aims to enhance robustness in Gradual Domain Adaptation (GDA) by addressing the challenge of smooth knowledge migration from the source to the target domain. Traditional GDA methods mitigate domain shift through intermediate domains and self-training but often suffer from inefficient knowledge migration or incomplete intermediate data. Our approach introduces a dynamic weighting mechanism that adaptively balances the loss contributions of the source and target domains during training. Specifically, we design an optimization framework governed by a time-varying hyperparameter $\varrho$ (progressing from 0 to 1), which controls the strength of domain-specific learning and ensures stable adaptation. The method leverages self-training to generate pseudo-labels and optimizes a weighted objective function for iterative model updates, maintaining robustness across intermediate domains. Experiments on rotated MNIST, color-shifted MNIST, portrait datasets, and the Cover Type dataset demonstrate that STDW outperforms existing baselines. Ablation studies further validate the critical role of $\varrho$'s dynamic scheduling in achieving progressive adaptation, confirming its effectiveness in reducing domain bias and improving generalization. This work provides both theoretical insights and a practical framework for robust gradual domain adaptation, with potential applications in dynamic real-world scenarios. The code is available at https://github.com/Dramwig/STDW.

However, selecting intermediate domains without explicit metadata remains a substantial challenge that has not been extensively explored in existing studies. T o tackle this issue, we propose a novel framework that combines reinforcement learning with feature disentanglement to conduct domain path selection in an unsupervised CDA setting. Our approach introduces an innovative unsupervised reward mechanism that leverages the distances between latent domain embeddings to facilitate the identification of optimal transfer paths. Furthermore, by disentangling features, our method facilitates the calculation of unsupervised rewards using domain-specific features and promotes domain adaptation by aligning domain-invariant features. This integrated strategy is designed to simultaneously optimize transfer paths and target task performance, enhancing the effectiveness of domain adaptation processes. Extensive empirical evaluations on datasets such as Rotated MNIST and ADNI demonstrate substantial improvements in prediction accuracy and domain selection efficiency, establishing our method's superiority over traditional CDA approaches.