Asynchronous Gradient Push

We consider a multiagent 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 multiagent 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 the state-of-the-art synchronous first-order methods, is more robust to failing or stalling agents, and scales better with the network size.

Automated summary

This study introduces a multiagent framework for distributed optimization, in which each agent accesses a local function and converges to the global minimum using an asynchronous algorithm. Numerical experiments demonstrate that asynchronous gradient push achieves faster global minimization and better scalability with network size compared to synchronous methods.