  Federated Learning (FL) is a distributed learning paradigm that enables a
large number of resource-limited nodes to collaboratively train a model without
data sharing. The non-independent-and-identically-distributed (non-i.i.d.) data
samples invoke discrepancies between the global and local objectives, making
the FL model slow to converge. In this paper, we proposed Optimal Aggregation
algorithm for better aggregation, which finds out the optimal subset of local
updates of participating nodes in each global round, by identifying and
excluding the adverse local updates via checking the relationship between the
local gradient and the global gradient. Then, we proposed a Probabilistic Node
Selection framework (FedPNS) to dynamically change the probability for each
node to be selected based on the output of Optimal Aggregation. FedPNS can
preferentially select nodes that propel faster model convergence. The
unbiasedness of the proposed FedPNS design is illustrated and the convergence
rate improvement of FedPNS over the commonly adopted Federated Averaging
(FedAvg) algorithm is analyzed theoretically. Experimental results demonstrate
the effectiveness of FedPNS in accelerating the FL convergence rate, as
compared to FedAvg with random node selection.
