Larger Offspring Populations Help the $(1 + (\lambda, \lambda))$ Genetic Algorithm to Overcome the Noise

• URL: http://arxiv.org/abs/2305.04553v1
• Date: Mon, 8 May 2023 08:49:01 GMT
• Title: Larger Offspring Populations Help the $(1 + (\lambda, \lambda))$ Genetic Algorithm to Overcome the Noise
• Authors: Alexandra Ivanova, Denis Antipov, Benjamin Doerr
• Abstract summary: Evolutionary algorithms are known to be robust to noise in the evaluation of the fitness. We analyze to what extent the $(lambda,lambda)$ genetic algorithm is robust to noise.
• Score: 76.24156145566425
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Evolutionary algorithms are known to be robust to noise in the evaluation of the fitness. In particular, larger offspring population sizes often lead to strong robustness. We analyze to what extent the $(1+(\lambda,\lambda))$ genetic algorithm is robust to noise. This algorithm also works with larger offspring population sizes, but an intermediate selection step and a non-standard use of crossover as repair mechanism could render this algorithm less robust than, e.g., the simple $(1+\lambda)$ evolutionary algorithm. Our experimental analysis on several classic benchmark problems shows that this difficulty does not arise. Surprisingly, in many situations this algorithm is even more robust to noise than the $(1+\lambda)$~EA.

Related papers

• Already Moderate Population Sizes Provably Yield Strong Robustness to Noise [53.27802701790209]
  We show that two evolutionary algorithms can tolerate constant noise probabilities without increasing the runtime on the OneMax benchmark. Our results are based on a novel proof argument that the noiseless offspring can be seen as a biased uniform crossover between the parent and the noisy offspring.
  arXiv  Detail & Related papers  (2024-04-02T16:35:52Z)
• Some Constructions of Private, Efficient, and Optimal $K$-Norm and Elliptic Gaussian Noise [54.34628844260993]
  Differentially private computation often begins with a bound on some $d$-dimensional statistic's sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using a norm tailored to the statistic's sensitivity space. This paper solves both problems for the simple statistics of sum, count, and vote.
  arXiv  Detail & Related papers  (2023-09-27T17:09:36Z)
• Near-Optimal Bounds for Learning Gaussian Halfspaces with Random Classification Noise [50.64137465792738]
  We show that any efficient SQ algorithm for the problem requires sample complexity at least $Omega(d1/2/(maxp, epsilon)2)$. Our lower bound suggests that this quadratic dependence on $1/epsilon$ is inherent for efficient algorithms.
  arXiv  Detail & Related papers  (2023-07-13T18:59:28Z)
• Runtime Analyses of Multi-Objective Evolutionary Algorithms in the Presence of Noise [7.421135890148154]
  We conduct the first analysis of a classic benchmark in the presence of noise in the objective functions. We prove that when bit-wise prior noise with rate $p le alpha/n$, $alpha$ a suitable constant is present. We prove that when all solutions are reevaluated in each iteration, then any noise rate $p = omega(log(n)/n2)$ leads to a super-polynomial runtime.
  arXiv  Detail & Related papers  (2023-05-17T14:48:06Z)
• Private estimation algorithms for stochastic block models and mixture models [63.07482515700984]
  General tools for designing efficient private estimation algorithms. First efficient $(epsilon, delta)$-differentially private algorithm for both weak recovery and exact recovery.
  arXiv  Detail & Related papers  (2023-01-11T09:12:28Z)
• Higher degree sum-of-squares relaxations robust against oblivious outliers [14.58610686291355]
  We consider estimation models of the form $Y=X*+N$, where $X*$ is some $m$-dimensional signal we wish to recover. We introduce a family of algorithms that under mild assumptions recover the signal $X*$ in all estimation problems for which there exists a sum-of-squares algorithm.
  arXiv  Detail & Related papers  (2022-11-14T13:09:12Z)
• Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation [58.24280149662003]
  We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. We develop new algorithms for list-decodable mean estimation, achieving nearly-optimal statistical guarantees.
  arXiv  Detail & Related papers  (2021-06-16T03:34:14Z)
• The $(1+(\lambda,\lambda))$ Genetic Algorithm for Permutations [0.0]
  We show that the $(lambda,lambda)$ genetic algorithm finds the optimum in $O(n2)$ fitness queries. We also present the first analysis of this algorithm on a permutation-based problem called Ham.
  arXiv  Detail & Related papers  (2020-04-18T17:04:57Z)
• Exponential Upper Bounds for the Runtime of Randomized Search Heuristics [9.853329403413701]
  We show that any of the algorithms randomized local search, algorithm, simulated annealing, and (1+1) evolutionary algorithm can optimize any pseudo-Boolean weakly monotonic function. We also prove an exponential upper bound for the runtime of the mutation-based version of the simple genetic algorithm on the OneMax benchmark.
  arXiv  Detail & Related papers  (2020-04-13T00:24:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.