# Improving exploration strategies in large dimensions and rate of convergence of global random search algorithms

arXiv: https://arxiv.org/abs/2208.11542 · HTML: https://mlsanity.com/paper/2208.11542/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [Fast PAC Global Optimization via Restarted Langevin: Exploration, Exploitation, and Degenerate Cooling](https://mlsanity.com/paper/2609.06196/) (2026)

## Abstract (arXiv)

We consider global optimization problems, where the feasible region X is a compact subset of ℝd with d ≥ 10. For these problems, we demonstrate the following. First: the actual convergence of global random search algorithms is much slower than that given by the classical estimates, based on the asymptotic properties of random points. Second: the usually recommended space exploration schemes are inefficient in the non-asymptotic regime. Specifically, (a) uniform sampling on entire~X is much less efficient than uniform sampling on a suitable subset of X, and (b) the effect of replacement of random points by low-discrepancy sequences is negligible.