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

arXiv: https://arxiv.org/abs/2209.03246 · HTML: https://mlsanity.com/paper/2209.03246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 6 Sep 2022.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Global optimization of Lipschitz functions](https://mlsanity.com/paper/1703.02628/) (2017)
- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [A simple parameter-free and adaptive approach to optimization under a minimal local smoothness assumption](https://mlsanity.com/paper/1810.00997/) (2018)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments](https://mlsanity.com/paper/2009.09249/) (2020)
- [Minimax Optimal Algorithms for Adversarial Bandit Problem with Multiple Plays](https://mlsanity.com/paper/1911.11122/) (2019)
- [Regret analysis of the Piyavskii-Shubert algorithm for global Lipschitz optimization](https://mlsanity.com/paper/2002.02390/) (2020)
- [Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions](https://mlsanity.com/paper/2201.07164/) (2022)
- [Cumulative Regret Analysis of the Piyavskii--Shubert Algorithm and Its Variants for Global Optimization](https://mlsanity.com/paper/2108.10859/) (2021)

## Abstract (arXiv)

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.