# Evolution Strategies Converges to Finite Differences

arXiv: https://arxiv.org/abs/2001.01684 · HTML: https://mlsanity.com/paper/2001.01684/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2019.

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

- [A Scalable Finite Difference Method for Deep Reinforcement Learning](https://mlsanity.com/paper/2210.07487/) (2022)
- [A Unified Perspective on Optimization in Machine Learning and Neuroscience: From Gradient Descent to Neural Adaptation](https://mlsanity.com/paper/2510.18812/) (2025)

## Abstract (arXiv)

Since the debut of Evolution Strategies (ES) as a tool for Reinforcement Learning by Salimans et al. 2017, there has been interest in determining the exact relationship between the Evolution Strategies gradient and the gradient of a similar class of algorithms, Finite Differences (FD).(Zhang et al. 2017, Lehman et al. 2018) Several investigations into the subject have been performed, investigating the formal motivational differences(Lehman et al. 2018) between ES and FD, as well as the differences in a standard benchmark problem in Machine Learning, the MNIST classification problem(Zhang et al. 2017). This paper proves that while the gradients are different, they converge as the dimension of the vector under optimization increases.