# Global Convergence of the (1+1) Evolution Strategy

arXiv: https://arxiv.org/abs/1706.02887 · HTML: https://mlsanity.com/paper/1706.02887/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2017.

## Built on by (most cited first, 2 of 2)

- [A Globally Convergent Evolutionary Strategy for Stochastic Constrained Optimization with Applications to Reinforcement Learning](https://mlsanity.com/paper/2202.10464/) (2022)
- [A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2502.17602/) (2025)

## Abstract (arXiv)

We establish global convergence of the (1+1) evolution strategy, i.e., convergence to a critical point independent of the initial state. More precisely, we show the existence of a critical limit point, using a suitable extension of the notion of a critical point to measurable functions. At its core, the analysis is based on a novel progress guarantee for elitist, rank-based evolutionary algorithms. By applying it to the (1+1) evolution strategy we are able to provide an accurate characterization of whether global convergence is guaranteed with full probability, or whether premature convergence is possible. We illustrate our results on a number of example applications ranging from smooth (non-convex) cases over different types of saddle points and ridge functions to discontinuous and extremely rugged problems.