  Federated learning (FL), as a distributed machine learning paradigm, promotes
personal privacy by clients' processing raw data locally. However, relying on a
centralized server for model aggregation, standard FL is vulnerable to server
malfunctions, untrustworthy server, and external attacks. To address this
issue, we propose a decentralized FL framework by integrating blockchain into
FL, namely, blockchain assisted decentralized federated learning (BLADE-FL). In
a round of the proposed BLADE-FL, each client broadcasts its trained model to
other clients, competes to generate a block based on the received models, and
then aggregates the models from the generated block before its local training
of the next round. We evaluate the learning performance of BLADE-FL, and
develop an upper bound on the global loss function. Then we verify that this
bound is convex with respect to the number of overall rounds K, and optimize
the computing resource allocation for minimizing the upper bound. We also note
that there is a critical problem of training deficiency, caused by lazy clients
who plagiarize others' trained models and add artificial noises to disguise
their cheating behaviors. Focusing on this problem, we explore the impact of
lazy clients on the learning performance of BLADE-FL, and characterize the
relationship among the optimal K, the learning parameters, and the proportion
of lazy clients. Based on the MNIST and Fashion-MNIST datasets, we show that
the experimental results are consistent with the analytical ones. To be
specific, the gap between the developed upper bound and experimental results is
lower than 5%, and the optimized K based on the upper bound can effectively
minimize the loss function.
