Federated semi-supervised learning (FSSL) has recently emerged as a promising approach for enhancing the performance of federated learning (FL) using ubiquitous unlabeled data. However, this approach encounters challenges when learning a global model using both fully labeled and fully unlabeled clients. Previous works overlook the dissimilarities between labeled and unlabeled clients, predominantly using shared parameters for local training across these two types of clients, thereby inducing intertask interference during local training. Moreover, these works typically adopt a single-perspective aggregation strategy, primarily focusing on data-volume-aware aggregation (i.e., FedAvg), leading to a lack of comprehensive consideration in model aggregation. In this article, we propose a novel FSSL method termed $\text {D}^{{2}}\text {Fed}$ , which addresses these issues by rethinking the roles of labeled clients and unlabeled ones to mitigate intertask interference during local training and by integrating client-type-aware with data-volume-aware to provide a more comprehensive perspective for model aggregation. Specifically, in local training, our proposed $\text {D}^{{2}}\text {Fed}$ distinguishes between the primary and accessory roles of labeled and unlabeled clients, respectively, performing dual-role additive local training (DALT) accordingly. In global aggregation, $\text {D}^{{2}}\text {Fed}$ uses a dual-perspective global aggregation (DGA) strategy, transitioning from data-volume-aware aggregation to client-type-aware aggregation. The proposed method simultaneously improves both local training and global model aggregation for FSSL without compromising privacy. We demonstrate the effectiveness and robustness of the proposed method through extensive experiments and elaborate ablation studies conducted on the CIFAR-10/100, SVHN, FMNIST, and STL-10 datasets. Experimental results show that $\text {D}^{{2}}\text {Fed}$ outperforms state-of-the-arts on five datasets under diverse data settings.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) *Non-uniqueness*: there are many different eigendecompositions of the same Laplacian, and (2) *Instability*: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be the use of "hard partition'' of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to ``softly partition'' eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods. Our code is available at https://github.com/Graph-COM/SPE.

We study the batched best arm identification (BBAI) problem, where the learner's goal is to identify the best arm while switching the policy as less as possible. In particular, we aim to find the best arm with probability $1-\delta$ for some small constant $\delta>0$ while minimizing both the sample complexity (total number of arm pulls) and the batch complexity (total number of batches). We propose the three-batch best arm identification (Tri-BBAI) algorithm, which is the first batched algorithm that achieves the optimal sample complexity in the asymptotic setting (i.e., $\delta\rightarrow 0$) and runs in $3$ batches in expectation. Based on Tri-BBAI, we further propose the almost optimal batched best arm identification (Opt-BBAI) algorithm, which is the first algorithm that achieves the near-optimal sample and batch complexity in the non-asymptotic setting (i.e., $1/\delta$ is finite), while enjoying the same batch and sample complexity as Tri-BBAI when $\delta$ tends to zero. Moreover, in the non-asymptotic setting, the complexity of previous batch algorithms is usually conditioned on the event that the best arm is returned (with a probability of at least $1-\delta$), which is potentially unbounded in cases where a sub-optimal arm is returned. In contrast, the complexity of Opt-BBAI does not rely on such an event. This is achieved through a novel procedure that we design for checking whether the best arm is eliminated, which is of independent interest.