Zeroth-order algorithms for stochastic distributed nonconvex optimization

In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being over n agents having access only to zeroth-order (ZO) information of cost. This has various machine learning applications. As solution, propose two ZO algorithms, in which at each iteration agent samples local oracle points time-varying smoothing parameter. We show that proposed algorithms achieve linear speedup convergence rate O(p/(nT)) for smooth functions under state-dependent variance assumptions are more general than commonly used bounded and Lipschitz assumptions, when global additionally satisfies Polyak–Łojasiewicz (P–Ł) condition, where p T dimension decision variable total number iterations, respectively. To best our knowledge, is first result algorithms. It consequently enables systematic processing performance improvements by adding agents. also converge linearly relatively second moment P–Ł condition. demonstrate through numerical experiments efficiency on generating adversarial examples from deep neural networks comparison baseline recently centralized