Table 1.

Notations and terminologies

Notation/tern	Description
$\mathbf{n}$	Number of devices
$T$	Number of global epochs
$H_{\tau }^i$	Number of local iterations in the ${\tau }^{\mathit{th}}$ epoch on the $i$th devices
$w_t$	Global model in the $t^{\mathit{th}}$ epoch on sever
$w_t^k$	The $k^{\mathit{th}}$ entry of $w_t$
$w_{\tau ,h}^i$	Model initialized from $w_{\tau }$, updated in the $h$th local iteration, on the $i$th device
$w_{\mathit{back}}^i$	the model before $w_{\mathrm{new}}^i$ is updated, on the $i$th devices
$c$	A hyper-parameter
$r$	A random number
$\vartheta$	A small constant
$\beta$	A magnitude coefficient
$D^i$	Dataset on the $i$th device
$z_{t,h}^i$	Data(minibatch) sampled from $D^i$
$\gamma$	Learning rate
Server	The place where the training data are placed
Worker	One worker on each device, process that trains the model