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Register a new userCovariance Matrix Adaptation Evolution Strategy Assisted by Principal Component Analysis
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Added by
Yangjie Mei
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Over the past decades, more and more methods gain a giant development due to the development of technology. Evolutionary Algorithms are widely used as a heuristic method. However, the budget of computation increases exponentially when the dimensions increase. In this paper, we will use the dimensionality reduction method Principal component analysis (PCA) to reduce the dimension during the iteration of Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is a good Evolutionary Algorithm that is presented as the numeric type and useful for different kinds of problems. We assess the performance of our new methods in terms of convergence rate on multi-modal problems from the Black-Box Optimization Benchmarking (BBOB) problem set and we also use the framework COmparing Continuous Optimizers (COCO) to see how the new method going and compare it to the other algorithms.
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This paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, saACM-ES, adjusts online the lifelength of the current surrogate model (the number of CMA-ES generations before learning a new surrogate) and the surrogate hyper-parameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speed-up of saACM-ES compared to the ACM-ES and CMA-ES baselines. The empirical validation of saACM-ES on the BBOB-2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.
Evolution-based neural architecture search requires high computational resources, resulting in long search time. In this work, we propose a framework of applying the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to the neural architecture search problem called CMANAS, which achieves better results than previous evolution-based methods while reducing the search time significantly. The architectures are modelled using a normal distribution, which is updated using CMA-ES based on the fitness of the sampled population. We used the accuracy of a trained one shot model (OSM) on the validation data as a prediction of the fitness of an individual architecture to reduce the search time. We also used an architecture-fitness table (AF table) for keeping record of the already evaluated architecture, thus further reducing the search time. CMANAS finished the architecture search on CIFAR-10 with the top-1 test accuracy of 97.44% in 0.45 GPU day and on CIFAR-100 with the top-1 test accuracy of 83.24% for 0.6 GPU day on a single GPU. The top architectures from the searches on CIFAR-10 and CIFAR-100 were then transferred to ImageNet, achieving the top-5 accuracy of 92.6% and 92.1%, respectively.
This paper addresses the development of a covariance matrix self-adaptation evolution strategy (CMSA-ES) for solving optimization problems with linear constraints. The proposed algorithm is referred to as Linear Constraint CMSA-ES (lcCMSA-ES). It uses a specially built mutation operator together with repair by projection to satisfy the constraints. The lcCMSA-ES evolves itself on a linear manifold defined by the constraints. The objective function is only evaluated at feasible search points (interior point method). This is a property often required in application domains such as simulation optimization and finite element methods. The algorithm is tested on a variety of different test problems revealing considerable results.
Fan et al. [$mathit{Annals}$ $mathit{of}$ $mathit{Statistics}$ $textbf{47}$(6) (2019) 3009-3031] proposed a distributed principal component analysis (PCA) algorithm to significantly reduce the communication cost between multiple servers. In this paper, we robustify their distributed algorithm by using robust covariance matrix estimators respectively proposed by Minsker [$mathit{Annals}$ $mathit{of}$ $mathit{Statistics}$ $textbf{46}$(6A) (2018) 2871-2903] and Ke et al. [$mathit{Statistical}$ $mathit{Science}$ $textbf{34}$(3) (2019) 454-471] instead of the sample covariance matrix. We extend the deviation bound of robust covariance estimators with bounded fourth moments to the case of the heavy-tailed distribution under only bounded $2+epsilon$ moments assumption. The theoretical results show that after the shrinkage or truncation treatment for the sample covariance matrix, the statistical error rate of the final estimator produced by the robust algorithm is the same as that of sub-Gaussian tails, when $epsilon geq 2$ and the sampling distribution is symmetric innovation. While $2 > epsilon >0$, the rate with respect to the sample size of each server is slower than that of the bounded fourth moment assumption. Extensive numerical results support the theoretical analysis, and indicate that the algorithm performs better than the original distributed algorithm and is robust to heavy-tailed data and outliers.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependence on the number of top principal components. We show that it can be used to give a fast iterative method for the popular principal component regression problem, giving the first major runtime improvement over the naive method of combining PCA with regression. To achieve our results, we first observe that ridge regression can be used to obtain a smooth projection onto the top principal components. We then sharpen this approximation to true projection using a low-degree polynomial approximation to the matrix step function. Step function approximation is a topic of long-term interest in scientific computing. We extend prior theory by constructing polynomials with simple iterative structure and rigorously analyzing their behavior under limited precision.
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