@article{Audet2023, 
author = {Charles Audet and Jean Bigeon and Romain Couderc and Michael Kokkolaras},
title = {Sequential stochastic blackbox optimization with zeroth-order gradient estimators},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {25922-25956},
keywords = {stochastic blackbox optimization, gradient approximation, sequential optimization, momentum-based method, convergence rate analysis},
url = {https://www.sciopen.com/article/10.3934/math.20231321},
doi = {10.3934/math.20231321},
abstract = {This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on sequential stochastic optimization (SSO), i.e., the original problem is decomposed into a sequence of subproblems. Each subproblem is solved by using a zeroth-order version of a sign stochastic gradient descent with momentum algorithm (i.e., ZO-signum) and with increasingly fine precision. This decomposition allows a good exploration of the space while maintaining the efficiency of the algorithm once it gets close to the solution. Under the Lipschitz continuity assumption on the blackbox, a convergence rate in mean is derived for the ZO-signum algorithm. Moreover, if the blackbox is smooth and convex or locally convex around its minima, the rate of convergence to an    ϵ-optimal point of the problem may be obtained for the SSO algorithm. Numerical experiments are conducted to compare the SSO algorithm with other state-of-the-art algorithms and to demonstrate its competitiveness.}
}