# Efficient Lipschitzian Global Optimization of H"older Continuous Multivariate Functions

arXiv: https://arxiv.org/abs/2303.14293 · HTML: https://mlsanity.com/paper/2303.14293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 24 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [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)
- [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)
- [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)
- [Efficient Minimax Optimal Global Optimization of Lipschitz Continuous Multivariate Functions](https://mlsanity.com/paper/2206.02383/) (2022)

## Abstract (arXiv)

This study presents an effective global optimization technique designed for multivariate functions that are H"older continuous. Unlike traditional methods that construct lower bounding proxy functions, this algorithm employs a predetermined query creation rule that makes it computationally superior. The algorithm's performance is assessed using the average or cumulative regret, which also implies a bound for the simple regret and reflects the overall effectiveness of the approach. The results show that with appropriate parameters the algorithm attains an average regret bound of O(T^-fracαn) for optimizing a H"older continuous target function with H"older exponent α in an n-dimensional space within a given time horizon T. We demonstrate that this bound is minimax optimal.