# Self-Adjusting Mutation Rates with Provably Optimal Success Rules

arXiv: https://arxiv.org/abs/1902.02588 · HTML: https://mlsanity.com/paper/1902.02588/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2019.

## Built on by (most cited first, 13 of 13)

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- [Theory-inspired Parameter Control Benchmarks for Dynamic Algorithm Configuration](https://mlsanity.com/paper/2202.03259/) (2022)
- [Effective Mutation Rate Adaptation through Group Elite Selection](https://mlsanity.com/paper/2204.04817/) (2022)
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- [Fourier Analysis Meets Runtime Analysis: Precise Runtimes on Plateaus](https://mlsanity.com/paper/2302.08021/) (2023)
- [Log-normal Mutations and their Use in Detecting Surreptitious Fake Images](https://mlsanity.com/paper/2409.15119/) (2024)
- [Multi-parameter Control for the (1+(λ,λ))-GA on OneMax via Deep Reinforcement Learning](https://mlsanity.com/paper/2505.12982/) (2025)
- [Tuning without Peeking: Provable Generalization Bounds and Robust LLM Post-Training](https://mlsanity.com/paper/2507.01752/) (2025)
- [SymMatika: Structure-Aware Symbolic Discovery](https://mlsanity.com/paper/2507.03110/) (2025)
- [Code World Models for Parameter Control in Evolutionary Algorithms](https://mlsanity.com/paper/2602.22260/) (2026)
- [Stein Variational Black-Box Combinatorial Optimization](https://mlsanity.com/paper/2604.15837/) (2026)
- [Discovering Interpretable Multi-Parameter Control Policies for Evolutionary Algorithms Using Deep Reinforcement Learning](https://mlsanity.com/paper/2606.10129/) (2026)

## Abstract (arXiv)

The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a family of success-based updated rules that are determined by an update strength F and a success rate. We analyze in this work how the performance of the (1+1) Evolutionary Algorithm on LeadingOnes depends on these two hyper-parameters. Our main result shows that the best performance is obtained for small update strengths F=1+o(1) and success rate 1/e. We also prove that the running time obtained by this parameter setting is, apart from lower order terms, the same that is achieved with the best fitness-dependent mutation rate. We show similar results for the resampling variant of the (1+1) Evolutionary Algorithm, which enforces to flip at least one bit per iteration.