$1D$ to $nD$: A Meta Algorithm for Multivariate Global Optimization via Univariate Optimizers
This work addresses a gap in optimization methods by enabling the use of simpler univariate tools for more complex multivariate problems, though it appears incremental as it builds on existing univariate techniques.
The authors tackled the problem of multivariate global optimization by proposing a meta algorithm that leverages univariate optimizers, showing it can directly solve such problems and providing regret bounds in terms of time horizon and univariate optimizer performance.
In this work, we propose a meta algorithm that can solve a multivariate global optimization problem using univariate global optimizers. Although the univariate global optimization does not receive much attention compared to the multivariate case, which is more emphasized in academia and industry; we show that it is still relevant and can be directly used to solve problems of multivariate optimization. We also provide the corresponding regret bounds in terms of the time horizon $T$ and the average regret of the univariate optimizer, when it is robust against nonnegative noises with robust regret guarantees.