ARGFree: A Randomized Gradient-Free algorithm for Aggregative Cooperative Optimization and Applications to Robotic Formation (Extended Version)

Aggregative cooperative optimization problems arise in distributed decision-making scenarios where each agent’s objective depends on its own decision as well as on an aggregate variable representing the collective behavior of the system. Motivated by practical settings in which gradient information is unavailable, this paper proposes a randomized gradient-free algorithm, named ARGFree, for solving such problems. We establish that ARGFree converges in expectation to an approximate optimizer, where the approximation error originates from the use of a randomized gradient estimator. To the best of our knowledge, ARGFree is the first method in the literature capable of solving aggregative cooperative optimization problems without requiring gradient information. The effectiveness of the proposed algorithm is validated through robotic formation control experiments, including an implementation on a team of embedded systems based on Segway-type robots.