检索结果-内蒙古大学图书馆

Open-loop and closed-loop solvabilities for discrete-time mean-field stochastic linear quadratic optimal control problems

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Song, Teng Liu, Bin Department of Mathematics Wuhan University of Technology China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

This paper discusses the discrete-time mean-field stochastic linear quadratic optimal control problems, whose weighting matrices in the cost functional are not assumed to be definite. The open-loop solvability is characterized by the existence of the solution to a mean-field forward-backward stochastic difference equations with a convexity condition and a stationary condition. The closed-loop solvability is presented by virtue of the existences of the regular solution to the generalized Riccati equations and the solution to the linear recursive equation, which is also shown by the uniform convexity of the cost functional. Moreover, based on a family of uniformly convex cost functionals, the finiteness of the problem is characterized. Also, it turns out that a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem. Finally, some examples are given to illustrate the theory *** Codes 93E20, 93C55, 49N10 Copyright © 2023, The Authors. All rights reserved.

关键词： Riccati equations

CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER–MARUYAMA METHOD

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Diancong, J.I.N. School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

This work focuses on the temporal average of the backward Euler–Maruyama (BEM) method, which is used to approximate the ergodic limit of stochastic ordinary differential equations with super-linearly growing drift coefficients. We give the central limit theorem (CLT) of the temporal average, which characterizes the asymptotics in distribution of the temporal average. When the deviation order is smaller than the optimal strong order, we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM method. For the case that the deviation order equals to the optimal strong order, the CLT is established via the Poisson equation associated with the generator of original equations. Numerical experiments are performed to illustrate the theoretical results. Copyright © 2023, The Authors. All rights reserved.

关键词： Poisson equation

A Decentralized Proximal Gradient Tracking Algorithm for Composite Optimization on Riemannian Manifolds

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Wang, Lei Bao, Le Liu, Xin Department of Statistics Pennsylvania State University University ParkPA United States State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches at present for tackling such composite optimization problems. The first, subgradient-based approaches, rely on subgradient information of the objective function to update variables, achieving an iteration complexity of O(ϵ-4 log2(ϵ-2)). The second, smoothing approaches, involve constructing a smooth approximation of the nonsmooth regularization term, resulting in an iteration complexity of O(ϵ-4). This paper proposes a proximal gradient type algorithm that fully exploits the composite structure. The global convergence to a stationary point is established with a significantly improved iteration complexity of O(ϵ-2). To validate the effectiveness and efficiency of our proposed method, we present numerical results in real-world applications, showcasing its superior performance. Copyright © 2024, The Authors. All rights reserved.

关键词： Iterative methods

STATIONARY FLUCTUATIONS FOR A MULTI-SPECIES ZERO RANGE PROCESS WITH LONG JUMPS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Zhao, Linjie School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We consider stationary fluctuations for the multi-species zero range process with long jumps in one dimension, where the underlying transition probability kernel is p(x) = c+|x|−1−α if x > 0 and = c−|x|−1−α if x ... 详细信息

关键词： Partial differential equations

Convergence analysis of Laguerre approximations for analytic functions

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Wang, Haiyong School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

Laguerre spectral approximations play an important role in the development of efficient algorithms for problems in unbounded domains. In this paper, we present a comprehensive convergence rate analysis of Laguerre spectral approximations for analytic functions. By exploiting contour integral techniques from complex analysis, we prove that Laguerre projection and interpolation methods of degree n converge at the root-exponential rate O(exp(−2ρ√n)) with ρ > 0 when the underlying function is analytic inside and on a parabola with focus at the origin and vertex at z = −ρ2. As far as we know, this is the first rigorous proof of root-exponential convergence of Laguerre approximations for analytic functions. Several important applications of our analysis are also discussed, including Laguerre spectral differentiations, Gauss-Laguerre quadrature rules, the scaling factor and the Weeks method for the inversion of Laplace transform, and some sharp convergence rate estimates are derived. Numerical experiments are presented to verify the theoretical *** Codes 41A25, 41A10 © 2023, CC BY-NC-SA.

关键词： Laplace transforms

The Error in Multivariate Linear Extrapolation with Applications to Derivative-Free Optimization

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Cao, Liyuan Wen, Zaiwen Yuan, Ya-Xiang Beijing International Center for Mathematical Research Peking University Beijing China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. However, linear extrapolation is used far more often in applications such as derivative-free optimization, while its error is not well-studied. We introduce in this paper a method to numerically compute the sharp bound on the error, and then present several analytical bounds along with the conditions under which they are sharp. We analyze in depth the approximation error achievable by quadratic functions and the error bound for the bivariate case. All results are under the assumptions that the function being interpolated has Lipschitz continuous gradient and is interpolated on an affinely independent sample set. © 2023, CC BY-NC-SA.

关键词： Interpolation

Fjord-Type AIEgens Based on Inherent Through-Space Conjugation

学校读者我要写书评

暂无评论

CCS Chemistry 2024年第7期6卷 1739-1747页

作者： Ye-Qiang Han Yuan Xie Jianyu Zhang Shiyu Tan Haoke Zhang Ben Zhong Tang Jonathan L.Sessler Feihe Huang Stoddart Institute of Molecular Science Department of ChemistryZhejiang UniversityHangzhou 310058 Zhejiang-Israel Joint Laboratory of Self-Assembling Functional Materials ZJU-Hangzhou Global Scientific and Technological Innovation CenterZhejiang UniversityHangzhou 311215 MOE Key Laboratory of Macromolecular Synthesis and Functionalization Department of Polymer Science and EngineeringZhejiang UniversityHangzhou 310058 Center for AIE Research College of Materials Science and EngineeringShenzhen UniversityShenzhen 518061 Department of Chemistry Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and ReconstructionThe Hong Kong University of Science and TechnologyKowloonHong Kong 999077 School of Science and Engineering Shenzhen Institute of Aggregate Science and TechnologyThe Chinese University of Hong KongShenzhen(CUHK-Shenzhen)Guangzhou 518172 Department of Chemistry The University of Texas at AustinAustinTexas 78712-1224 Green Catalysis Center and College of Chemistry Zhengzhou UniversityZhengzhou 450001

Through-space conjugation(TSC)is a noncovalently electronic interaction that is emerging as a potential complement to through-bond conjugation(TBC)-based strategies for constructing luminescent ***,the design of efficient luminogens based on TSC is currently challenging due to a lack of established structure-property *** is particularly true in the case of luminogens displaying aggregation-induced emission(AIE)*** this work,three terphenyl derivatives were prepared,and their photophysical properties were systemically *** was found that relative to the corresponding m-and p-linked analogues,the electronic interaction of TBC is weakened while the strength of TSC is commensurately enhanced in the constitutional isomer containing an o-linked fjordtype *** this set of luminogens,the presence of a fjord-type arrangement promotes a transformation from aggregation-caused quenching to *** investigations involving congeneric quaterphenyl and pentphenyl isomers support the universality of the fjord-type unit as a framework for synthesizing AIE-active luminogens(AIEgens)with inherent *** work not only provides a novel set of AIEgens but also establishes the utility of TSC in controlling the photophysical properties of nonconventional and twisted luminogens.

关键词： fjord-type through-space conjugation through-bond conjugation aggregation-induced emission luminescence twisted conformation

t-PSI: Efficient Multi-party Private Set Intersection with Threshold 19

学校读者我要写书评

暂无评论

t-PSI: Efficient Multi-party Private Set Intersection with T...

2022 IEEE SmartWorld, 19th IEEE International Conference on Ubiquitous Intelligence and computing, 2022 IEEE International Conference on Autonomous and Trusted Vehicles Conference, 22nd IEEE International Conference on Scalable computing and Communications, 2022 IEEE International Conference on Digital Twin, 8th IEEE International Conference on Privacy computing and 2022 IEEE International Conference on Metaverse, SmartWorld/UIC/ATC/ScalCom/DigitalTwin/PriComp/Metaverse 2022

作者： Meng, Dan Fu, Zhihui Kong, Chao Qi, Yue Cao, Guitao Oppo Research Institute Shenzhen China Anhui Polytechnic University School of Computer and Information Wuhu China East China Normal University Shanghai Key Laboratory of Trustworthy Computing Shanghai China MoE Engineering Research Center of SH/HW Co-design Technology and Application Ecnu Shanghai China

ISBN: (纸本)9798350346558

Multi-party privacy set intersection (MPSI) enables multiple parties to compute the intersection of their datasets without leaking data privacy. Among existing MPSI protocols, e.g., KMPRT-based protocols, oblivious evaluation of programmable pseudo-random function (OPPRF) or oblivious pseudo-random function (OPRF) is typically used to generate pseudo random numbers, requiring frequent online interactions. To mitigate such communication overheads, we propose the threshold Privacy Set Intersection (t-PSI) protocol for multi-party, leveraging the Shamir Secret Sharing (SSS) protocol and the masking construction mechanism. We propose two types of masking construction mechanisms: Polynomial and Garbled Bloom-filter. To the best of our knowledge, this is the first Secret Sharing-based MPSI protocol. With the significant reduction of inter-party communication, the t-PSI protocol is highly scalable and can handle datasets ranging from 26 to 220. Further, with built-in fault tolerance, t-PSI works even if some parties went offline during protocol execution. As shown in the experiments, for five parties with datasets of 220 items each, the proposed t-PSI takes only 63 seconds, outperforming the state-of-the-art in [1]. © 2022 IEEE.

关键词： Fault tolerance

When Adversarial Example Attacks Meet Vertical Federated Learning 19

学校读者我要写书评

暂无评论

When Adversarial Example Attacks Meet Vertical Federated Lea...

ISBN: (纸本)9798350346558

Federated learning (FL) is proposed to enable efficient machine learning while protecting the privacy of user data. In non-federated scenarios, machine learning models are vulnerable to adversarial attacks. The attacker can construct elaborate adversarial examples, which can greatly reduce the performance of the victim model. It is worth exploring how FL models differ from traditional models in face of complex adversarial attacks. We are also curious about the robustness of different FL modeling methods against adversarial attacks, providing suggestions for selecting suitable FL models in practical applications. Consequently, we perform adversarial example attacks on vertical federated learning and design experiments to study how vertical federated models perform under adversarial example attacks. The simulation results show that federated models are more robust than non-federated models. Besides, in vertical federation learning, decision trees and XGBoost are much more robust than logistic regression and neural networks. © 2022 IEEE.

关键词： Decision trees