  Edge devices can benefit remarkably from federated learning due to their
distributed nature; however, their limited resource and computing power poses
limitations in deployment. A possible solution to this problem is to utilize
off-the-shelf sparse learning algorithms at the clients to meet their resource
budget. However, such naive deployment in the clients causes significant
accuracy degradation, especially for highly resource-constrained clients. In
particular, our investigations reveal that the lack of consensus in the
sparsity masks among the clients may potentially slow down the convergence of
the global model and cause a substantial accuracy drop. With these
observations, we present \textit{federated lottery aware sparsity hunting}
(FLASH), a unified sparse learning framework for training a sparse sub-model
that maintains the performance under ultra-low parameter density while yielding
proportional communication benefits. Moreover, given that different clients may
have different resource budgets, we present \textit{hetero-FLASH} where clients
can take different density budgets based on their device resource limitations
instead of supporting only one target parameter density. Experimental analysis
on diverse models and datasets shows the superiority of FLASH in closing the
gap with an unpruned baseline while yielding up to $\mathord{\sim}10.1\%$
improved accuracy with $\mathord{\sim}10.26\times$ fewer communication,
compared to existing alternatives, at similar hyperparameter settings. Code is
available at \url{https://github.com/SaraBabakN/flash_fl}.
