  Federated learning (FL) is a new machine learning framework which trains a
joint model across a large amount of decentralized computing devices. Existing
methods, e.g., Federated Averaging (FedAvg), are able to provide an
optimization guarantee by synchronously training the joint model, but usually
suffer from stragglers, i.e., IoT devices with low computing power or
communication bandwidth, especially on heterogeneous optimization problems. To
mitigate the influence of stragglers, this paper presents a novel FL algorithm,
namely Hybrid Federated Learning (HFL), to achieve a learning balance in
efficiency and effectiveness. It consists of two major components: synchronous
kernel and asynchronous updater. Unlike traditional synchronous FL methods, our
HFL introduces the asynchronous updater which actively pulls unsynchronized and
delayed local weights from stragglers. An adaptive approximation method,
Adaptive Delayed-SGD (AD-SGD), is proposed to merge the delayed local updates
into the joint model. The theoretical analysis of HFL shows that the
convergence rate of the proposed algorithm is $\mathcal{O}(\frac{1}{t+\tau})$
for both convex and non-convex optimization problems.
