Title: Federated Semi-supervised Learning with Dual Regulator. Abstract: Federated learning emerges as a powerful method to learn from decentralized heterogeneous data while protecting data privacy. Federated semi-supervised learning (FSSL) is even more practical and challenging, where only a fraction of data can be labeled due to high annotation cost. Existing FSSL methods, however, assume independent and identically distributed (IID) labeled data across clients and consistent class distribution between labeled and unlabeled data within a client. In this work, we propose a novel FSSL framework with dual regulator, FedDure, to optimize and customize model training according to specific data distributions of clients. FedDure lifts the previous assumption with a coarse-grained regulator (C-reg) and a fine-grained regulator (F-reg): C-reg regularizes the updating of local model by tracking the learning effect on labeled data distribution; F-reg learns an adaptive weighting scheme tailored for unlabeled instances in each client. We further formulate the client model training as bi-level optimization that adaptively optimize the model in the client with two regulators. Theoretically, we show the convergence guarantee of dual regulator. Empirically, we demonstrate that FedDure is superior to the existing methods across wide range of settings, notably by more than 12% on CIFAR-10 and CINIC-10 datasets.