Direct-search methods for decentralized blackbox optimization

Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. In this paper, we adapt direct-search methods, a classical technique in derivative-free optimization, to the decentralized setting. In contrast with zeroth-order algorithms, our algorithms rely on positive spanning sets to define suitable search directions while still possessing global convergence guaranties, thanks to carefully chosen stepsizes. Numerical experiments highlight the advantages of direct-search techniques over gradient-approximation-based strategies.