  We develop a Distributed Event-Triggered Stochastic GRAdient Descent
(DETSGRAD) algorithm for solving non-convex optimization problems typically
encountered in distributed deep learning. We propose a novel communication
triggering mechanism that would allow the networked agents to update their
model parameters aperiodically and provide sufficient conditions on the
algorithm step-sizes that guarantee the asymptotic mean-square convergence. The
algorithm is applied to a distributed supervised-learning problem, in which a
set of networked agents collaboratively train their individual neural networks
to recognize handwritten digits in images, while aperiodically sharing the
model parameters with their one-hop neighbors. Results indicate that all agents
report similar performance that is also comparable to the performance of a
centrally trained neural network, while the event-triggered communication
provides significant reduction in inter-agent communication. Results also show
that the proposed algorithm allows the individual agents to recognize the
digits even though the training data corresponding to all the digits are not
locally available to each agent.
