In FL setting, the goal is typically to minimize the following objective function:

$mi{n}_{w}F(w),$ where $F(w)$:$={\displaystyle \underset{k=1}{\overset{m}{}}}{p}_k{F}_k(w)$

Here $m$ is the total number of devices, $F_k$ is the local objective function for the $k$ th device, and $p_k$ specifies the relative impact of

each device with $p_{k}0$ and ${\displaystyle \underset{k=1.m}{\overset{?}{}}}{p}_k=1.$ What happens to the global objective function $F(w)$ when $p_k=\frac{1}{m}?$ Is this strategy

good in the presence of slowly responding devices?