Learning Stochastic Graph Neural Networks With Constrained Variance

Stochastic graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. SGNNs trained with respect to the expected performance, which comes no guarantee about deviations of particular output realizations around optimal expectation. To overcome this issue, we propose a variance-constrained optimization problem for SGNNs, balancing performance and stochastic deviation. An alternating primal-dual learning procedure is undertaken solves by updating SGNN parameters gradient descent dual variable ascent. characterize explicit effect learning, conduct theoretical analysis on variance identify trade-off between robustness discrimination power. We further analyze duality gap converging behavior procedure. The former indicates optimality loss induced transformation latter characterizes limiting error iterative algorithm, both learning. Through numerical simulations, corroborate our findings observe strong controllable standard