A Natural Evolution Strategy for Multi-objective Optimization

Glasmachers, Tobias; Schaul, Tom; Schmidhuber, Juergen

doi:10.1007/978-3-642-15844-5_63

Cited by 19 publications

(26 citation statements)

References 11 publications

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“…Natural Evolution Strategies (NES) [31,28,27,11,10,25] have been derived as population-based variants and as hill-climbers from the simple and powerful principle to adapt the search distribution in order to optimize (here, minimize) expected fitness by means of natural gradient descent. This general paradigm can be applied to all kinds of search distributions.…”

Section: Evolution Strategiesmentioning

confidence: 99%

“…This general paradigm can be applied to all kinds of search distributions. Gaussians with different subsets of adaptive parameters have been treated in the literature, such as adaptation of the full covariance matrix [31,28,27,11,10] and diagonal covariance matrices [25].…”

Section: Evolution Strategiesmentioning

confidence: 99%

“…The corresponding hill-climber variant (1+1)-xNES primarily differs in its step size adaptation rule [10]. Success-based utility values (which are rank-based in the sense of (1+1) selection) are used to implement a success-based selfadaptation rule, resulting in a behavior close to Rechenberg's 1/5-rule [24].…”

Section: Evolution Strategiesmentioning

confidence: 99%

“…Modern, flexible, and easy to implement natural evolution strategies [31,28,27,11,10,25] are used as search algorithms for kernel representations of continuous functions of a single variable (time). The efficiency is demonstrated on the problem of finding kinematic plan representations for redundant robot arms movement.…”

Section: Introductionmentioning

confidence: 99%

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Kernel representations for evolving continuous functions

2012

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Abstract. To parameterize continuous functions for evolutionary learning, we use kernel expansions in nested sequences of function spaces of growing complexity. This approach is particularly powerful when dealing with non-convex constraints and discontinuous objective functions. Kernel methods offer a number of beneficial properties for parameterizing continuous functions, such as smoothness and locality, which make them attractive as a basis for mutation operators. Beyond such practical considerations, kernel methods make heavy use of inner products in function space and offer a well established regularization framework. We show how evolutionary computation can profit from these properties. Searching function spaces of iteratively increasing complexity allows the solution to evolve from a simple first guess to a complex and highly refined function. At transition points where the evolution strategy is confronted with the next level of functional complexity, the kernel framework can be used to project the search distribution into the extended search space. The feasibility of the method is demonstrated on challenging trajectory planning problems where redundant robots have to avoid obstacles.

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Section: Evolution Strategiesmentioning

confidence: 99%

Section: Evolution Strategiesmentioning

confidence: 99%

Section: Evolution Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kernel representations for evolving continuous functions

2012

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“…The paper is organized as follows. We start with an introduction to the general NES scheme, including two recent variants, the exponential version (xNES, [3]) and the hillclimber version [2]. We then introduce SNES with its computationally efficient updates, and generalize NES to heavytailed search distributions.…”

Section: Introductionmentioning

confidence: 99%

High dimensions and heavy tails for natural evolution strategies

Schaul

Glasmachers

Schmidhuber

2011

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

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The family of natural evolution strategies (NES) offers a principled approach to real-valued evolutionary optimization by following the natural gradient of the expected fitness on the parameters of its search distribution. While general in its formulation, existing research has focused only on multivariate Gaussian search distributions. We address this shortcoming by exhibiting problem classes for which other search distributions are more appropriate, and then derive the corresponding NES-variants.First, we show how simplifying NES to separable distributions reduces its complexity from O(d 3 ) to O(d), and apply it to problems of previously unattainable dimensionality, recovering lowest-energy structures on the Lennard-Jones atom clusters and state-of-the-art results on neuro-evolution benchmarks. Second, we develop a new, equivalent formulation based on invariances, which allows us to generalize NES to heavy-tailed distributions, even if their variance is undefined. We then investigate how this variant aids in overcoming deceptive local optima.

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Motion Capture and Contemporary Optimization Algorithms for Robust and Stable Motions on Simulated Biped Robots

Seekircher

Stoecker

Abeyruwan

et al. 2013

RoboCup 2012: Robot Soccer World Cup XVI

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Biped soccer robots have shown drastic improvements in motion skills over the past few years. Still, a lot of work needs to be done with the RoboCup Federation's vision of 2050 in mind. One goal is creating a workflow for quickly generating reliable motions, preferably with inexpensive and accessible hardware. Our hypothesis is that using Microsoft's Kinect sensor in combination with a modern optimization algorithm can achieve this objective. We produced four complex and inherently unstable motions and then applied three contemporary optimization algorithms (CMA-ES, xNES, PSO) to make the motions robust; we performed 900 experiments with these motions on a 3D simulated Nao robot with full physics. In this paper we describe the motion mapping technique, compare the optimization algorithms, and discuss various basis functions and their impact on the learning performance. Our conclusion is that there is a straightforward process to achieve complex and stable motions in a short period of time.

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A Natural Evolution Strategy for Multi-objective Optimization

Cited by 19 publications

References 11 publications

Kernel representations for evolving continuous functions

Kernel representations for evolving continuous functions

High dimensions and heavy tails for natural evolution strategies

Motion Capture and Contemporary Optimization Algorithms for Robust and Stable Motions on Simulated Biped Robots

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