Convergence of Unregularized Online Learning Algorithms

In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess generalization errors in expectation. A sufficient condition for the almost sure convergence is also given. With high probability, we provide explicit convergence rates of the excess generalization errors for both averaged iterates and the last iterate, which in turn also imply convergence rates with probability one. To our best knowledge, this is the first high-probability convergence rate for the last iterate of online gradient descent algorithms without strong convexity. Without any boundedness assumptions on iterates, our results are derived by a novel use of two measures of the algorithm's one-step progress, respectively by generalization errors and by distances in RKHSs, where the variances of the involved martingales are cancelled out by the descent property of the algorithm

DomainDrop: Suppressing Domain-Sensitive Channels for Domain Generalization

Deep Neural Networks have exhibited considerable success in various visual tasks. However, when applied to unseen test datasets, state-of-the-art models often suffer performance degradation due to domain shifts. In this paper, we introduce a novel approach for domain generalization from a novel perspective of enhancing the robustness of channels in feature maps to domain shifts. We observe that models trained on source domains contain a substantial number of channels that exhibit unstable activations across different domains, which are inclined to capture domain-specific features and behave abnormally when exposed to unseen target domains. To address the issue, we propose a DomainDrop framework to continuously enhance the channel robustness to domain shifts, where a domain discriminator is used to identify and drop unstable channels in feature maps of each network layer during forward propagation. We theoretically prove that our framework could effectively lower the generalization bound. Extensive experiments on several benchmarks indicate that our framework achieves state-of-the-art performance compared to other competing methods. Our code is available at https://github.com/lingeringlight/DomainDrop.Comment: Accepted by ICCV2023. The code is available at https://github.com/lingeringlight/DomainDro

ALOFT: A Lightweight MLP-like Architecture with Dynamic Low-frequency Transform for Domain Generalization

Domain generalization (DG) aims to learn a model that generalizes well to unseen target domains utilizing multiple source domains without re-training. Most existing DG works are based on convolutional neural networks (CNNs). However, the local operation of the convolution kernel makes the model focus too much on local representations (e.g., texture), which inherently causes the model more prone to overfit to the source domains and hampers its generalization ability. Recently, several MLP-based methods have achieved promising results in supervised learning tasks by learning global interactions among different patches of the image. Inspired by this, in this paper, we first analyze the difference between CNN and MLP methods in DG and find that MLP methods exhibit a better generalization ability because they can better capture the global representations (e.g., structure) than CNN methods. Then, based on a recent lightweight MLP method, we obtain a strong baseline that outperforms most state-of-the-art CNN-based methods. The baseline can learn global structure representations with a filter to suppress structure irrelevant information in the frequency space. Moreover, we propose a dynAmic LOw-Frequency spectrum Transform (ALOFT) that can perturb local texture features while preserving global structure features, thus enabling the filter to remove structure-irrelevant information sufficiently. Extensive experiments on four benchmarks have demonstrated that our method can achieve great performance improvement with a small number of parameters compared to SOTA CNN-based DG methods. Our code is available at https://github.com/lingeringlight/ALOFT/.Comment: Accepted by CVPR2023. The code is available at https://github.com/lingeringlight/ALOFT