An illustration is provided inFigure 6. Asshowninalgorithm 1,there arethree main steps intheoverall procedure: first, we construct the coarse domain sequence by learning to predict the domain score for each example and sorting the examples according to the domain scores.

Gradual Domain Adaptation (GDA), in which the learner is provided with additional intermediate domains, has been theoretically and empirically studied in many contexts. Despite its vital role in security-critical scenarios, the adversarial robustness of the GDA model remains unexplored. In this paper, we adopt the effective gradual self-training method and replace vanilla self-training with adversarial self-training (AST). AST first predicts labels on the unlabeled data and then adversarially trains the model on the pseudo-labeled distribution. Intriguingly, we find that gradual AST improves not only adversarial accuracy but also clean accuracy on the target domain.

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.

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions.

Existing literature lacks a graph domain adaptation technique for handling large distribution shifts, primarily due to the difficulty in simulating an evolving path from source to target graph. To make a breakthrough, we present a graph gradual domain adaptation (GGDA) framework with the construction of a compact domain sequence that minimizes information loss in adaptations. Our approach starts with an efficient generation of knowledge-preserving intermediate graphs over the Fused Gromov-Wasserstein (FGW) metric. With the bridging data pool, GGDA domains are then constructed via a novel vertex-based domain progression, which comprises "close" vertex selections and adaptive domain advancement to enhance inter-domain information transferability. Theoretically, our framework concretizes the intractable inter-domain distance $W_p(\mu_t,\mu_{t+1})$ via implementable upper and lower bounds, enabling flexible adjustments of this metric for optimizing domain formation. Extensive experiments under various transfer scenarios validate the superior performance of our GGDA framework.

Gradual Domain Adaptation (GDA), in which the learner is provided with additional intermediate domains, has been theoretically and empirically studied in many contexts. Despite its vital role in security-critical scenarios, the adversarial robustness of the GDA model remains unexplored. In this paper, we adopt the effective gradual self-training method and replace vanilla self-training with adversarial self-training (AST). AST first predicts labels on the unlabeled data and then adversarially trains the model on the pseudo-labeled distribution. Intriguingly, we find that gradual AST improves not only adversarial accuracy but also clean accuracy on the target domain.

Recently, sharpness-aware minimization (SAM) has emerged as a promising method to improve generalization by minimizing sharpness, which is known to correlate well with generalization ability. Since the original proposal of SAM, many variants of SAM have been proposed to improve its accuracy and efficiency, but comparisons have mainly been restricted to the i.i.d. setting. In this paper we study SAM for out-of-distribution (OOD) generalization. First, we perform a comprehensive comparison of eight SAM variants on zero-shot OOD generalization, finding that the original SAM outperforms the Adam baseline by $4.76\%$ and the strongest SAM variants outperform the Adam baseline by $8.01\%$ on average. We then provide an OOD generalization bound in terms of sharpness for this setting. Next, we extend our study of SAM to the related setting of gradual domain adaptation (GDA), another form of OOD generalization where intermediate domains are constructed between the source and target domains, and iterative self-training is done on intermediate domains, to improve the overall target domain error. In this setting, our experimental results demonstrate that the original SAM outperforms the baseline of Adam on each of the experimental datasets by $0.82\%$ on average and the strongest SAM variants outperform Adam by $1.52\%$ on average. We then provide a generalization bound for SAM in the GDA setting. Asymptotically, this generalization bound is no better than the one for self-training in the literature of GDA. This highlights a further disconnection between the theoretical justification for SAM versus its empirical performance, with recent work finding that low sharpness alone does not account for all of SAM's generalization benefits. For future work, we provide several potential avenues for obtaining a tighter analysis for SAM in the OOD setting.

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of $T\ge2$ data distributions $P_1,\ldots,P_T$ undergoing a gradual shift, where each pair of consecutive measures $P_i,P_{i+1}$ are close to each other in Wasserstein distance. We have a supervised dataset of size $n$ sampled from $P_0$, while for the subsequent distributions in the sequence, only unlabeled i.i.d. samples are available. Moreover, we assume that all distributions exhibit a known favorable attribute, such as (but not limited to) having intra-class soft/hard margins. In this context, we propose a methodology rooted in Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius. We theoretically show that this method guarantees the classification error across all $P_i$s can be suitably bounded. Our bounds rely on a newly introduced {\it {compatibility}} measure, which fully characterizes the error propagation dynamics along the sequence. Specifically, for inadequately constrained distributions, the error can exponentially escalate as we progress through the gradual shifts. Conversely, for appropriately constrained distributions, the error can be demonstrated to be linear or even entirely eradicated. We have substantiated our theoretical findings through several experimental results.