  This paper considers a distributed stochastic non-convex optimization
problem, where the nodes in a network cooperatively minimize a sum of
$L$-smooth local cost functions with sparse gradients. By adaptively adjusting
the stepsizes according to the historical (possibly sparse) gradients, a
distributed adaptive gradient algorithm is proposed, in which a gradient
tracking estimator is used to handle the heterogeneity between different local
cost functions. We establish an upper bound on the optimality gap, which
indicates that our proposed algorithm can reach a first-order stationary
solution dependent on the upper bound on the variance of the stochastic
gradients. Finally, numerical examples are presented to illustrate the
effectiveness of the algorithm.
