Extremum Seeking Tracking for Derivative-free Distributed Optimization

In this paper, we deal with a network of agents that want to cooperatively minimize the sum of local cost functions depending on a common decision variable. We consider the challenging scenario in which objective functions are unknown and agents have only access to local measurements of their local function. We propose a novel distributed algorithm which combines a gradient tracking policy with an extremum seeking technique to estimate the global descent direction. The joint use of these two techniques results in a distributed optimization scheme which is proven to provide arbitrarily accurate solution estimate through the combination of Lyapunov and averaging analysis approaches with consensus theory. To corroborate the theoretical results, we perform numerical simulations in a personalized optimization framework and a cooperative robotics scenario.