A weak tail-bound probabilistic condition for function estimation in stochastic derivative-free optimization

Abstract

In this paper, we use tail bounds to define a tailored probabilistic condition for function estimation that eases the theoretical analysis of stochastic derivative-free optimization methods. In particular, we focus on the unconstrained minimization of a potentially non-smooth function, whose values can only be estimated via stochastic observations, and give a simplified convergence proof for both a direct search and a basic trust-region scheme.