  We consider a multi-agent framework for distributed optimization where each
agent has access to a local smooth strongly convex function, and the collective
goal is to achieve consensus on the parameters that minimize the sum of the
agents' local functions. We propose an algorithm wherein each agent operates
asynchronously and independently of the other agents. When the local functions
are strongly-convex with Lipschitz-continuous gradients, we show that the
iterates at each agent converge to a neighborhood of the global minimum, where
the neighborhood size depends on the degree of asynchrony in the multi-agent
network. When the agents work at the same rate, convergence to the global
minimizer is achieved. Numerical experiments demonstrate that Asynchronous
Gradient-Push can minimize the global objective faster than state-of-the-art
synchronous first-order methods, is more robust to failing or stalling agents,
and scales better with the network size.
