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In this work, we propose a meta algorithm that can solve a multivariateglobal optimization problem using univariate global optimizers. Although theunivariate global optimization does not receive much attention compared to themultivariate case, which is more emphasized in academia and industry; we showthat it is still relevant and can be directly used to solve problems ofmultivariate optimization. We also provide the corresponding regret bounds interms of the time horizon $T$ and the average regret of the univariateoptimizer, when it is robust against nonnegative noises with robust regretguarantees.

$1D$ to $nD$: A Meta Algorithm for Multivariate Global Optimization via Univariate Optimizers