D-(DP)²SGD: Decentralized Parallel SGD with Differential Privacy in Dynamic Networks

Table 1

Frequently used notations.

Notation	Description
	The vector norm or the matrix spectral norm depending on the argument
	The matrix Frobenius norm
	The optimization function
	The gradient of a function
	The column vector in with for all elements
	The optimal solution of problem
	The th largest eigenvalue of a matrix
	The network topology at iterate
	The set of nodes
	The set of edges at iterate
	The total number of iterations
	The set of neighbors of node at iterate
	The local variable in node at iterate
	The average local variable with all nodes at iterate
	The sampled training data in node at iterate
	The perturbed variable in node at iterate
	The Laplace noise drawn from
	The concatenation of all local variables
	The concatenation of all perturbed variables
	The concatenation of all Laplace noises
	The concatenation of all random samples
	The concatenation of all stochastic gradients