# Natural Evolution Strategies

@article{Wierstra2008NaturalES, title={Natural Evolution Strategies}, author={Daan Wierstra and Tom Schaul and Jan Peters and Juergen Schmidhuber}, journal={2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)}, year={2008}, pages={3381-3387} }

This paper presents natural evolution strategies (NES), a novel algorithm for performing real-valued dasiablack boxpsila function optimization: optimizing an unknown objective function where algorithm-selected function measurements constitute the only information accessible to the method. Natural evolution strategies search the fitness landscape using a multivariate normal distribution with a self-adapting mutation matrix to generate correlated mutations in promising regions. NES shares this… Expand

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Implementation of "Exponential Natural Evolution Strategies" (xNES) https://arxiv.org/abs/1106.4487

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#### 533 Citations

Exponential natural evolution strategies

- Mathematics, Computer Science
- GECCO '10
- 2010

The new algorithm, exponential NES (xNES), is significantly simpler than its predecessors and is more principled than CMA-ES, as all the update rules needed for covariance matrix adaptation are derived from a single principle. Expand

Mirror Natural Evolution Strategies

- Computer Science, Mathematics
- ArXiv
- 2019

It is shown that the estimated covariance matrix of MiNES converges to the inverse of Hessian matrix of the objective function with a sublinear convergence rate, which proves that MiNES is a query-efficient optimization algorithm competitive to classical algorithms including NES and CMA-ES. Expand

Information-Geometric Optimization with Natural Selection

- Biology, Computer Science
- Entropy
- 2020

The relationship between classical population genetics of quantitative traits and evolutionary optimization, and a new evolutionary algorithm that combines natural selection, recombination operator, and an adaptive method to increase selection and find the optimum are detailed. Expand

A Natural Evolution Strategy for Multi-objective Optimization

- Computer Science
- PPSN
- 2010

This paper derives a (1+1) hillclimber version of NES which is then used as the core component of a multi-objective optimization algorithm and finds it to be competitive with the state-of-the-art. Expand

Proposal of distance-weighted exponential natural evolution strategies

- Mathematics, Computer Science
- 2011 IEEE Congress of Evolutionary Computation (CEC)
- 2011

DX-NES remedies two problems of a conventional method, the exponential natural evolution strategies, that shows good performance when it does not need to move the distribution for sampling individuals down the slope to the optimal point, and outperformed the xNES on all the benchmark functions. Expand

Self-Guided Evolution Strategies with Historical Estimated Gradients

- Computer Science, Psychology
- IJCAI
- 2020

A new ES algorithm SGES is proposed, which utilizes historical estimated gradients to construct a low-dimensional subspace for sampling search directions, and adjusts the importance of this subspace adaptively, and proves that the variance of the gradient estimator of SGES can be much smaller than that of Vanilla ES. Expand

Efficient Natural Evolution Strategies Evolution Strategies and Evolutionary Programming Track

- Biology
- 2009

Efficient Natural Evolution Strategies (eNES) uses a fast algorithm to calculate the inverse of the exact Fisher in- formation matrix, thus increasing both robustness and per- formance of its evolution gradient estimation, even in higher dimensions. Expand

Adaptive Stochastic Natural Gradient Method for Optimizing Functions with Low Effective Dimensionality

- Computer Science
- PPSN
- 2020

The proposed method suppresses the natural gradient elements with the low SNRs, helping to accelerate the learning rate adaptation in ASNG and is incorporated into the cGA and demonstrated on the benchmark functions of binary optimization. Expand

Efficient natural evolution strategies

- Computer Science, Mathematics
- GECCO
- 2009

Efficient Natural Evolution Strategies (eNES) uses a fast algorithm to calculate the inverse of the exact Fisher information matrix, thus increasing both robustness and performance of its evolution gradient estimation, even in higher dimensions. Expand

Evolution Strategies

- Computer Science
- Handbook of Computational Intelligence
- 2015

In this overview the important concepts of success based step-size control, self-adaptation and derandomization are covered, as well as more recent developments like covariance matrix adaptation and natural evolution strategies that give new insights into the fundamental mathematical rationale behind evolution strategies. Expand

#### References

SHOWING 1-10 OF 100 REFERENCES

Exponential natural evolution strategies

- Mathematics, Computer Science
- GECCO '10
- 2010

The new algorithm, exponential NES (xNES), is significantly simpler than its predecessors and is more principled than CMA-ES, as all the update rules needed for covariance matrix adaptation are derived from a single principle. Expand

A Natural Evolution Strategy for Multi-objective Optimization

- Computer Science
- PPSN
- 2010

This paper derives a (1+1) hillclimber version of NES which is then used as the core component of a multi-objective optimization algorithm and finds it to be competitive with the state-of-the-art. Expand

Efficient natural evolution strategies

- Computer Science, Mathematics
- GECCO
- 2009

Efficient Natural Evolution Strategies (eNES) uses a fast algorithm to calculate the inverse of the exact Fisher information matrix, thus increasing both robustness and performance of its evolution gradient estimation, even in higher dimensions. Expand

Completely Derandomized Self-Adaptation in Evolution Strategies

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This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation and reveals local and global search properties of the evolution strategy with and without covariance matrix adaptation. Expand

Stochastic search using the natural gradient

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- ICML '09
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The Natural Gradient is used to update the distribution's parameters in the direction of higher expected fitness, by efficiently calculating the inverse of the exact Fisher information matrix whereas previous methods had to use approximations. Expand

Toward a Theory of Evolution Strategies: Self-Adaptation

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This paper analyzes the self-adaptation (SA) algorithm widely used to adapt strategy parameters of the evolution strategy (ES) in order to obtain maximal ES performance and shows that applying Schwefel's -scaling rule guarantees the linear convergence order of the ES. Expand

Analysis of a Simple Evolutionary Algorithm for Minimization in Euclidean Spaces

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It is proved that the commonly used "Gauss mutations" in combination with the so-called 1/5-rule for the mutation adaptation do achieve asymptotically optimalexp ected runtime. Expand

Algorithmic analysis of a basic evolutionary algorithm for continuous optimization

- Computer Science, Mathematics
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It turns out that, in the scenario considered, Gaussian mutations in combination with the 1/5-rule indeed ensure asymptotically optimal runtime; namely, Θ(n) steps/function evaluations are necessary and sufficient to halve the approximation error. Expand

Improving Evolution Strategies through Active Covariance Matrix Adaptation

- Mathematics, Computer Science
- 2006 IEEE International Conference on Evolutionary Computation
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A novel modification to the derandomised covariance matrix adaptation algorithm used in connection with evolution strategies to use information about unsuccessful offspring candidate solutions in order to actively reduce variances of the mutation distribution in unpromising directions of the search space. Expand

Bidirectional Relation between CMA Evolution Strategies and Natural Evolution Strategies

- Computer Science
- PPSN
- 2010

This paper derives the explicit form of the natural gradient of the expected fitness and transforms it into the forms corresponding to the mean vector and the covariance matrix of the mutation distribution to show that the natural evolution strategy can be viewed as a variant of covariance Matrix adaptation evolution strategies using Cholesky update. Expand