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Consensus-Based Optimization Methods Converge Globally

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arXiv 2021年

作者： Fornasier, Massimo Klock, Timo Riedl, Konstantin Technical University of Munich School of Computation Information and Technology Department of Mathematics Munich Germany Munich Center for Machine Learning Munich Germany Munich Data Science Institute Munich Germany Simula Research Laboratory Department of Numerical Analysis and Scientific Computing Oslo Norway University of San Diego Department of Mathematics San DiegoCA United States

In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on an experimentally supported intuition that, on average, CBO performs a gradient descent of the squared Euclidean distance to the global minimizer, we devise a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions. The result unveils internal mechanisms of CBO that are responsible for the success of the method. In particular, we prove that CBO performs a convexification of a large class of optimization problems as the number of optimizing agents goes to infinity. Furthermore, we improve prior analyses by requiring mild assumptions about the initialization of the method and by covering objectives that are merely locally Lipschitz continuous. As a core component of this analysis, we establish a quantitative nonasymptotic Laplace principle, which may be of independent interest. From the result of CBO convergence in mean-field law, it becomes apparent that the hardness of any global optimization problem is necessarily encoded in the rate of the mean-field approximation, for which we provide a novel probabilistic quantitative estimate. The combination of these results allows to obtain probabilistic global convergence guarantees of the numerical CBO *** Codes 65K10, 90C26, 90C56, 35Q90, 35Q84 Copyright © 2021, The Authors. All rights reserved.

关键词： Fokker Planck equation

Primal Characterizations of Stability of Error Bounds for Semi-infinite Convex Constraint Systems in Banach Spaces

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arXiv 2023年

作者： Wei, Zhou Théra, Michel Yao, Jen-Chih Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding071002 China XLIM UMR CNRS 7252 Université de Limoges Limoges France Federation University Australia Ballarat Australia Research Center for Interneural Computing China Medical University Hospital China Medical University Taichung Taiwan

This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are subject to small perturbations. These characterizations are given in terms of the directional derivatives of the functions that enter into the definition of these systems. It is proved that the stability of error bounds is essentially equivalent to verifying that the optimal values of several minimax problems, defined in terms of the directional derivatives of the functions defining these systems, are outside of some neighborhood of zero. Moreover, such stability only requires that all component functions entering the system have the same linear perturbation. When these stability results are applied to the sensitivity analysis of Hoffman’s constants for semi-infinite linear systems, primal criteria for Hoffman’s constants to be uniformly bounded under perturbations of the problem data are *** Codes 90C31, 90C25, 49J52, 46B20 © 2023, CC0.

关键词： Sensitivity analysis

Cooperative Co-evolution for large scale optimization through more frequent random grouping

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Cooperative Co-evolution for large scale optimization throug...

Congress on Evolutionary Computation

作者： Mohammad Nabi Omidvar Xiaodong Li Zhenyu Yang Xin Yao Evolutionary Computing and Machine Learning Group (ECML) the School of Computer Science and IT RMIT University Melbourne VIC Australia Nature Inspired Computation and Application Laboratory Department of Computer Science and Technology University of Science and Technology Hefei Anhui China Centre of Excellence of Research in Computational Intelligence and Applications (CERCIA) School of Computer Science University of Binningham Birmingham UK

In this paper we propose three techniques to improve the performance of one of the major algorithms for large scale continuous global function optimization. Multilevel Cooperative Co-evolution (MLCC) is based on a Cooperative Co-evolutionary framework and employs a technique called random grouping in order to group interacting variables in one subcomponent. It also uses another technique called adaptive weighting for co-adaptation of subcomponents. We prove that the probability of grouping interacting variables in one subcomponent using random grouping drops significantly as the number of interacting variables increases. This calls for more frequent random grouping of variables. We show how to increase the frequency of random grouping without increasing the number of fitness evaluations. We also show that adaptive weighting is ineffective and in most cases fails to improve the quality of found solution, and hence wastes considerable amount of CPU time by extra evaluations of objective function. Finally we propose a new technique for self-adaptation of the subcomponent sizes in CC. We demonstrate how a substantial improvement can be gained by applying these three techniques.

关键词： Optimization Probability Computer science Electronic mail Space exploration Computational modeling Software

Perturbation Analysis of Error Bounds for Convex Functions on Banach Spaces

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arXiv 2024年

作者： Wei, Zhou Théra, Michel Yao, Jen-Chih Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding071002 China XLIM UMR CNRS 7252 Université de Limoges Limoges France Research Center for Interneural Computing China Medical University Hospital China Medical University Taichung Taiwan Academy of Romanian Scientists Bucharest50044 Romania

This paper focuses on the stability of both local and global error bounds for a proper lower semicontinuous convex function defined on a Banach space. Without relying on any dual space information, we first provide precise estimates of error bound moduli using directional derivatives. For a given proper lower semicontinuous convex function on a Banach space, we prove that the stability of local error bounds under small perturbations is equivalent to the directional derivative at a reference point having a non-zero minimum over the unit sphere. Additionally, the stability of global error bounds is shown to be equivalent to the infimum of the directional derivatives, at all points on the boundary of the solution set, being bounded away from zero over some neighborhood of the unit sphere. © 2024, CC0.

关键词： Banach spaces

Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces

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arXiv 2023年

作者： Wei, Zhou Théra, Michel Yao, Jen-Chih Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding071002 China XLIM UMR CNRS 7252 Université de Limoges Limoges France Research Center for Interneural Computing China Medical University Hospital China Medical University Taichung Taiwan Academy of Romanian Scientists Bucharest50044 Romania

In this paper, we mainly study subtransversality and two types of strong CHIP (given via Fréchet and limiting normal cones) for a collection of finitely many closed sets. We first prove characterizations of Asplund spaces in terms of subtransversality and intersection formulae of Fréchet normal cones. Several necessary conditions for subtransversality of closed sets are obtained via Fréchet/limiting normal cones in Asplund spaces. Then, we consider subtransversality for some special closed sets in convex-composite optimization. In this frame we prove an equivalence result on subtransversality, strong Fréchet CHIP and property (G) so as to extend a duality characterization of subtransversality of finitely many closed convex sets via strong CHIP and property (G) to the possibly non-convex case. As applications, we use these results on subtransversality and strong CHIP to study error bounds of inequality systems and give several dual criteria for error bounds via Fréchet normal cones and subdifferentials. © 2023, CC0.

关键词： Convex optimization

Deep Sensor Fusion with Pyramid Fusion Networks for 3D Semantic Segmentation

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Deep Sensor Fusion with Pyramid Fusion Networks for 3D Seman...

IEEE Symposium on Intelligent Vehicle

作者： Hannah Schieber Fabian Duerr Torsten Schoen Jü rgen Beyerer Human-Centered Computing and Extended Reality Friedrich-Alexander University (FAU) Erlangen-N&#x00FC rnberg Erlangen Germany Vision and Fusion Laboratory Karlsruhe Institute of Technology Karlsruhe Germany Research Institute Almotion Bavaria Technische Hochschule Ingolstadt Ingolstadt Germany Fraunhofer Institute of Optronics System Technologies and Image Exploitation (IOSB) Fraunhofer Center of Machine Learning Karlsruhe Germany

Robust environment perception for autonomous vehicles is a tremendous challenge, which makes a diverse sensor set with e.g. camera, lidar and radar crucial. In the process of understanding the recorded sensor data, 3D semantic segmentation plays an important role. Therefore, this work presents a pyramid-based deep fusion architecture for lidar and camera to improve 3D semantic segmentation of traffic scenes. Individual sensor backbones extract feature maps of camera images and lidar point clouds. A novel Pyramid Fusion Backbone fuses these feature maps at different scales and combines the multimodal features in a feature pyramid to compute valuable multimodal, multi-scale features. The Pyramid Fusion Head aggregates these pyramid features and further refines them in a late fusion step, incorporating the final features of the sensor backbones. The approach is evaluated on two challenging outdoor datasets and different fusion strategies and setups are investigated. It outperforms recent range view based lidar approaches as well as all so far proposed fusion strategies and architectures.

关键词： Point cloud compression Image segmentation Laser radar Three-dimensional displays Head Fuses Semantics

Decision-based black-box attack against vision transformers via patch-wise adversarial removal 22

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Decision-based black-box attack against vision transformers ...

Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Yucheng Shi Yahong Han Yu-an Tan Xiaohui Kuang College of Intelligence and Computing and Tianjin Key Lab of Machine Learning Tianjin University Tianjin China and Engineering Research Center of City Intelligence and Digital Governance Ministry of Education of the People's Republic of China School of Cyberspace Science and Technology Beijing Institute of Technology Beijing China National Key Laboratory of Science and Technology on Information System Security Beijing China

ISBN: (纸本)9781713871088

Vision transformers (ViTs) have demonstrated impressive performance and stronger adversarial robustness compared to Convolutional Neural Networks (CNNs). On the one hand, ViTs' focus on global interaction between individual patches reduces the local noise sensitivity of images. On the other hand, the neglect of noise sensitivity differences between image regions by existing decision-based attacks further compromises the efficiency of noise compression, especially for ViTs. Therefore, validating the black-box adversarial robustness of ViTs when the target model can only be queried still remains a challenging problem. In this paper, we theoretically analyze the limitations of existing decision-based attacks from the perspective of noise sensitivity difference between regions of the image, and propose a new decision-based black-box attack against ViTs, termed Patch-wise Adversarial Removal (PAR). PAR divides images into patches through a coarse-to-fine search process and compresses the noise on each patch separately. PAR records the noise magnitude and noise sensitivity of each patch and selects the patch with the highest query value for noise compression. In addition, PAR can be used as a noise initialization method for other decision-based attacks to improve the noise compression efficiency on both ViTs and CNNs without introducing additional calculations. Extensive experiments on three datasets demonstrate that PAR achieves a much lower noise magnitude with the same number of queries.

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GSLB: The Graph Structure learning Benchmark 37

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GSLB: The Graph Structure Learning Benchmark

37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Li, Zhixun Wang, Liang Sun, Xin Luo, Yifan Zhu, Yanqiao Chen, Dingshuo Luo, Yingtao Zhou, Xiangxin Liu, Qiang Wu, Shu Yu, Jeffrey Xu Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong Center for Research on Intelligent Perception and Computing State Key Laboratory of Multimodal Artificial Intelligence Systems Institute of Automation Chinese Academy of Sciences China School of Artificial Intelligence University of Chinese Academy of Sciences China Department of Automation University of Science and Technology of China China School of Cyberspace Security Beijing University of Posts and Telecommunications China Department of Computer Science University of California Los Angeles United States Heinz College of Information Systems and Public Policy Machine Learning Department School of Computer Science Carnegie Mellon University United States

ISBN: (纸本)9781713899921

Graph Structure learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://***/GSL-Benchmark/GSLB. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Graphic methods

Predicting Response to Patients with Gastric Cancer Via a Dynamic-Aware Model with Longitudinal Liquid Biopsy Data

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SSRN

SSRN 2024年

作者： Chen, Zifan Zhao, Jie Li, Yanyan Li, Yilin Liu, Huimin Feng, Xujiao Nan, Xinyu Dong, Bin Shen, Lin Chen, Yang Zhang, Li Center for Data Science Peking University Beijing China Department of Gastrointestinal Oncology Key Laboratory of Carcinogenesis and Translational Research Ministry of Education Peking University Cancer Hospital and Institute Beijing China National Engineering Laboratory for Big Data Analysis and Applications Peking University Beijing China Guangzhou Medical University Guangzhou China Peking University Beijing China Center for Machine Learning Research Peking University Beijing China Peking University Changsha Institute for Computing and Digital Economy Changsha China

Gastric cancer (GC) presents challenges in predicting treatment responses due to its patient-specific heterogeneity. Recently, liquid biopsies have become recognized as a valuable data modality, offering essential cellular and molecular insights and enabling the capture of time-sensitive information. This study aimed to harness artificial intelligence (AI) technology to analyze longitudinal liquid biopsy data. We collected a dataset from longitudinal liquid biopsies of 91 patients at Peking Cancer Hospital, spanning from July 2019 to April 2022, which included 1,895 tumor-related cellular images and 1,698 tumor marker indices. Subsequently, we introduced the Dynamic-Aware Model (DAM) to predict GC treatment responses. DAM incorporates the dynamic data through AI-engineered components, enabling an in-depth longitudinal analysis. Utilizing three-fold cross-validation, DAM exhibited superior performance over traditional cell-counting-based methods, achieving an AUC of 0.807 in predicting GC treatment responses. In the test set, DAM maintained stable efficacy with an AUC of 0.802. Besides, DAM showed the capability to accurately predict treatment responses from early treatment data. Moreover, DAM's visual analysis of attention mechanisms identified six dynamic focus-area-related visual features and their strong association with treatment response. These findings represent a pioneering effort in applying AI technology for interpreting longitudinal liquid biopsy data and employ visual analytics in GC, offering a promising avenue toward precise response prediction and tailored treatment strategies for patients with ***: This work was supported by the National Natural Science Foundation of China (81801778 to Li Zhang., 82203881 to Yang Chen, U22A20327 to Lin Shen, 12090022 to Bin Dong), Beijing Natural Science Foundation (7222021 to Yang Chen), Beijing Hospitals Authority Youth Programme (QML20231115 to Yang Chen), Clinical Medicine Plus X-Young Scholars Project of P

关键词： Diseases