  Federated learning (FL) aims to train machine learning models in the
decentralized system consisting of an enormous amount of smart edge devices.
Federated averaging (FedAvg), the fundamental algorithm in FL settings,
proposes on-device training and model aggregation to avoid the potential heavy
communication costs and privacy concerns brought by transmitting raw data.
However, through theoretical analysis we argue that 1) the multiple steps of
local updating will result in gradient biases and 2) there is an inconsistency
between the expected target distribution and the optimization objectives
following the training paradigm in FedAvg. To tackle these problems, we first
propose an unbiased gradient aggregation algorithm with the keep-trace gradient
descent and the gradient evaluation strategy. Then we introduce an additional
controllable meta updating procedure with a small set of data samples,
indicating the expected target distribution, to provide a clear and consistent
optimization objective. Both the two improvements are model- and task-agnostic
and can be applied individually or together. Experimental results demonstrate
that the proposed methods are faster in convergence and achieve higher accuracy
with different network architectures in various FL settings.
