Asynchronous Gradient-Push
For multi-agent distributed optimization, this work provides an asynchronous algorithm that is more robust and scalable than synchronous methods.
The paper proposes an asynchronous distributed optimization algorithm for multi-agent networks with smooth strongly convex functions, showing convergence to a neighborhood of the global minimum depending on asynchrony, and faster convergence than synchronous methods in experiments.
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.