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This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex…

Machine Learning · Computer Science 2023-03-13 Nikolaus Hansen

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost…

Neural and Evolutionary Computing · Computer Science 2014-06-12 Ilya Loshchilov , Marc Schoenauer , Michèle Sebag , Nikolaus Hansen

Water distribution system design is a challenging optimisation problem with a high number of search dimensions and constraints. In this way, Evolutionary Algorithms (EAs) have been widely applied to optimise WDS to minimise cost subject…

Neural and Evolutionary Computing · Computer Science 2019-09-12 Mehdi Neshat , Bradley Alexander , Angus Simpson

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a popular method to deal with nonconvex and/or stochastic optimization problems when the gradient information is not available. Being based on the CMA-ES, the recently proposed…

Neural and Evolutionary Computing · Computer Science 2017-05-19 Ilya Loshchilov , Tobias Glasmachers , Hans-Georg Beyer

In several real-world applications in medical and control engineering, there are unsafe solutions whose evaluations involve inherent risk. This optimization setting is known as safe optimization and formulated as a specialized type of…

Neural and Evolutionary Computing · Computer Science 2024-05-20 Kento Uchida , Ryoki Hamano , Masahiro Nomura , Shota Saito , Shinichi Shirakawa

We introduce an acceleration for covariance matrix adaptation evolution strategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). This diagonal acceleration endows the default CMA-ES with the advantages of separable CMA-ES…

Neural and Evolutionary Computing · Computer Science 2019-05-16 Youhei Akimoto , Nikolaus Hansen

Various variants of the well known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) have been proposed recently, which improve the empirical performance of the original algorithm by structural modifications. However, in practice it…

Neural and Evolutionary Computing · Computer Science 2018-08-20 Sander van Rijn , Hao Wang , Matthijs van Leeuwen , Thomas Bäck

In this study, we consider simulation-based worst-case optimization problems with continuous design variables and a finite scenario set. To reduce the number of simulations required and increase the number of restarts for better local…

Neural and Evolutionary Computing · Computer Science 2022-12-01 Atsuhiro Miyagi , Kazuto Fukuchi , Jun Sakuma , Youhei Akimoto

Embedding & MLP has become a paradigm for modern large-scale recommendation system. However, this paradigm suffers from the cold-start problem which will seriously compromise the ecological health of recommendation systems. This paper…

Information Retrieval · Computer Science 2022-05-30 Xu Zhao , Yi Ren , Ying Du , Shenzheng Zhang , Nian Wang

An emerging line of work has shown that machine-learned predictions are useful to warm-start algorithms for discrete optimization problems, such as bipartite matching. Previous studies have shown time complexity bounds proportional to some…

Machine Learning · Computer Science 2023-02-03 Shinsaku Sakaue , Taihei Oki

Generative models like diffusion and flow-matching create high-fidelity samples by progressively refining noise. The refinement process is notoriously slow, often requiring hundreds of function evaluations. We introduce Warm-Start Diffusion…

Machine Learning · Computer Science 2025-09-30 Jonas Scholz , Richard E. Turner

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active,…

Machine Learning · Computer Science 2021-01-01 Jordan T. Ash , Ryan P. Adams

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…

Neural and Evolutionary Computing · Computer Science 2021-05-12 Yangjie Mei , Hao Wang

Hyperparameters of deep neural networks are often optimized by grid search, random search or Bayesian optimization. As an alternative, we propose to use the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is known for its…

Neural and Evolutionary Computing · Computer Science 2016-04-26 Ilya Loshchilov , Frank Hutter

This paper presents a new optimization approach to causal estimation. Given data that contains covariates and an outcome, which covariates are causes of the outcome, and what is the strength of the causality? In classical machine learning…

Methodology · Statistics 2024-10-22 Mingzhang Yin , Yixin Wang , David M. Blei

Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a highly effective optimization technique. A primary challenge when applying CMA-ES in high dimensionality is sampling from a multivariate normal distribution with an arbitrary…

Neural and Evolutionary Computing · Computer Science 2026-01-05 Jarosław Arabas , Adam Stelmaszczyk , Eryk Warchulski , Dariusz Jagodziński , Rafał Biedrzycki

Recent research in Cooperative Coevolution~(CC) have achieved promising progress in solving large-scale global optimization problems. However, existing CC paradigms have a primary limitation in that they require deep expertise for selecting…

Machine Learning · Computer Science 2025-04-25 Hongshu Guo , Wenjie Qiu , Zeyuan Ma , Xinglin Zhang , Jun Zhang , Yue-Jiao Gong

We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical…

Neural and Evolutionary Computing · Computer Science 2014-04-23 Ilya Loshchilov

We focus on the challenge of finding a diverse collection of quality solutions on complex continuous domains. While quality diver-sity (QD) algorithms like Novelty Search with Local Competition (NSLC) and MAP-Elites are designed to generate…

Machine Learning · Computer Science 2020-05-08 Matthew C. Fontaine , Julian Togelius , Stefanos Nikolaidis , Amy K. Hoover

One of the most challenging types of ill-posedness in global optimization is the presence of insensitivity regions in design parameter space, so the identification of their shape will be crucial, if ill-posedness is irrecoverable. Such…

Neural and Evolutionary Computing · Computer Science 2019-05-20 Jakub Sawicki , Maciej Smołka , Marcin Łoś , Robert Schaefer