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Routing Among Convex Polygonal Obstacles in the Plane

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2024年第6期35卷 723-739页

作者： Inkulu, R. Kumar, Pawan IIT Guwahati Dept Comp Sci & Enginnering Gauhati India

Given a set P of h pairwise disjoint convex polygonal obstacles in the plane, defined with n vertices, we preprocess P and compute one routing table at each vertex in a subset of vertices of P. For routing a packet from any vertex s ? P to any vertex t ? P, our scheme computes a routing path with a multiplicative stretch 1 + E and an additive stretch 2kg, by consulting routing tables at only a subset of vertices along that path. Here, k is the number of obstacles of P the routing path intersects, and P depends on the geometry of obstacles in P. During the preprocessing phase, we construct routing tables of size O(n + h(3) /?(2) polylog (h/? )) in O(n + h(3) /?(2) polylog (h/? )) time, where ? < 1 is an input parameter.

关键词： Computational geometry shortest paths approximation algorithms

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Resilient Constrained Optimization in Multi-Agent Systems With Improved Guarantee on approximation Bounds

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 2659-2664页

作者： Kaheni, Mojtaba Usai, Elio Franceschelli, Mauro Univ Cagliari Dept Elect & Elect Engn I-91123 Cagliari Italy

This letter considers resilient decentralized constrained optimization in multi-agent systems where some agents due to cyberattacks become adversaries. We show that the proposed method is resilient despite the persistent influence of up to F anonymous adversaries in the complete graphs. Our approach provides a better approximation of the optimal solution than the current literature. If the agents' objectives are 2F redundant, then the algorithm converges to the optimal solution. In addition to current literature, we consider a constrained optimization problem. Finally, we present numerical simulations to corroborate the theoretical analysis.

关键词： Optimization Multi-agent systems Convergence approximation algorithms Optical filters Linear programming Cost function Cyber-physical security distributed optimization multi-agent systems resilient optimization

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Investigating the Resilience Source of Classification Systems for Approximate Computing Techniques

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IEEE Transactions on Emerging Topics in Computing 2024年 1-12页

作者： Barbareschi, Mario Barone, Salvatore Department of Electrical Engineering and Information Technologies University of Naples Federico II Naples Italy

During the last decade, classification systems (CSs) received significant research attention, with new learning algorithms achieving high accuracy in various applications. However, their resource-intensive nature, in terms of hardware and computation time, poses new design challenges. CSs exhibit inherent error resilience, due to redundancy of training sets, and self-healing properties, making them suitable for Approximate Computing (AxC). AxC enables efficient computation by using reduced precision or approximate values, leading to energy, time, and silicon area savings. Exploiting AxC involves estimating the introduced error for each approximate variant found during a Design-Space Exploration (DSE). This estimation has to be both rapid and meaningful, considering a substantial number of test samples, which are utterly conflicting demands. In this paper, we investigate on sources of error resiliency of CSs, and we propose a technique to haste the DSE that reduces the computational time for error estimation by systematically reducing the test set. In particular, we cherry-pick samples that are likely to be more sensitive to approximation and perform accuracy-loss estimation just by exploiting such a sample subset. In order to demonstrate its efficacy, we integrate our technique into two different approaches for generating approximate CSs, showing an average speed-up up to 18. Authors

关键词： approximation algorithms

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Neural network methods based on efficient optimization algorithms for solving impulsive differential equations

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2024年第3期5卷 1067-1076页

作者： Xing, Baixue Liu, Hongliang Tang, Xiao Shi, Long School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China School of Computational Science and Electronics Hunan Institute of Engineering Xiangtan411105 China

In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a physics-informed neural network method combined with learning rate attenuation strategy to solve linear impulsive differential equations and nonlinear impulsive differential equations, respectively. For the linear impulsive differential equations, first, the interval is segmented according to the impulse points, and a single hidden layer neural network model is constructed, the weight parameters of the hidden layer are randomly set, the optimal output parameters, and solution of the first segment are obtained by the extreme learning machine algorithm, then we calculate the initial value of the second segment according to the jumping equation and the remaining segments are solved in turn in the same way. Although the single hidden layer neural network method proposed can solve linear equations with high accuracy, it is not suitable for solving nonlinear equations. Therefore, we propose the physics-informed neural network combined with a learning rate attenuation strategy to solve the nonlinear impulsive differential equations, then the Adam algorithm and L-BFGS algorithm are combined to find the optimal approximate solution of each segment. Numerical examples show that the single hidden layer neural network method with Legendre polynomials as the activation function and the physics-informed neural network method combined with learning rate attenuation strategy can solve linear and nonlinear impulsive differential equations with higher accuracy. Impact Statement-It is difficult to obtain the analytical solutions of impulsive differential equations because of the existence of impulse points, and the current numerical methods are complicated and demanding. In recent years, artificial neural network methods have been widely used due to its simplicity and efficie

关键词： approximation algorithms

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Generalized Unitary Approximate Message Passing for Double Linear Transformation Model

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 1524-1538页

作者： Mo, Linlin Lu, Xinhua Yuan, Jide Zhang, Chuanzong Wang, Zhongyong Popovski, Petar Zhengzhou Univ Sch Elect & Informat Engn Zhengzhou 450001 Peoples R China Nanyang Inst Technol Coll Informat Engn Nanyang 473000 Peoples R China Soochow Univ Sch Elect & Informat Engn Suzhou 215006 Peoples R China Aalborg Univ Dept Elect Syst DK-9220 Aalborg Denmark

The double linear transformation model Y = AXB + W plays an important role in a variety of science and engineering applications, where X is estimated through known transformation matrices A and B from the noisy measurement Y. Decoupling X from Y is a formidable task due to the high complexity brought by the multiplication of the unknown matrix (vector) with the transformation matrix (M-UMTM). Unitary approximate message passing (UAMP) has been verified as a low complexity and strong robustness solution to the M-UMTM problems. However, it has only been used to tackle the problems with a single linear transformation matrix. In this work, we develop a generalized algorithm, namely, generalized double UAMP (GD-UAMP) for the target model, which not only inherits the low complexity of AMP, but also enhances robustness by employing double unitary transformation. As a generalized algorithm, GD-UAMP can be applied to address the generalized Bayesian inference problem, i.e., the arbitrary prior probability of X and likelihood function of Z, where Z = AXB is the noiseless measurement. We verify the feasibility of the proposed algorithm in the channel estimation problem for various wireless communication systems. Numerical results demonstrate that the proposed algorithm can perfectly fit different scenarios and showcase superior performance compared with benchmarks.

关键词： Signal processing algorithms approximation algorithms Message passing Complexity theory Inference algorithms Mathematical models Bayes methods Approximate message passing (AMP) channel estimation message passing Reconfigurable intelligent surface (RIS) unitary transformation

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Local Linear Convergence of Infeasible Optimization With Orthogonal Constraints

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 2727-2732页

作者： Sun, Youbang Chen, Shixiang Garcia, Alfredo Shahrampour, Shahin Northeastern Univ Dept Mech & Ind Engn Boston MA 02115 USA Univ Sci & Technol China Minist Educ Math Fdn & Applicat Digital Technol Sch Math Sci Hefei 230027 Peoples R China Univ Sci & Technol China Minist Educ Math Fdn & Applicat Digital Technol Key Lab Hefei 230027 Peoples R China Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77845 USA

Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the Stiefel manifold, which can be computationally expensive. Recently, an infeasible retraction-free approach, termed the landing algorithm, was proposed as an efficient alternative. Motivated by the common occurrence of orthogonality constraints in tasks such as principle component analysis and training of deep neural networks, this letter studies the landing algorithm and establishes a novel linear convergence rate for smooth non-convex functions using only a local Riemannian P & Lstrok;condition. Numerical experiments demonstrate that the landing algorithm performs on par with the state-of-the-art retraction-based methods with substantially reduced computational overhead.

关键词： Manifolds Optimization Convergence Safety approximation algorithms Training Principal component analysis Machine learning Linear programming Heuristic algorithms Riemannian optimization orthogonality constraints infeasible methods linear convergence

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A PARALLEL approximation ALGORITHM FOR MINIMUM AREA POLYGONIZATION BASED ON CLUSTERING

UPB Scientific Bulletin, Series C: Electrical Engineering an...

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UPB Scientific Bulletin, Series C: Electrical Engineering and Computer Science 2022年第2期84卷 111-122页

作者： Asaeedi, Saeed Shamaee, Mahsa Soheil Department of Computer Science Faculty of Mathematical Sciences University of Kashan Kashan87317-53153 Iran

Minimum area polygonization is a well-known NP-complete problem in computational geometry. It is the problem of finding a simple polygon with minimum area for a given set of points in the plane. We present a parallel approximation algorithm based on clustering to solve this problem in polynomial time. The algorithm has four phases: clustering the points into the meaningful parts, reclustering the big clusters to the smaller ones, finding minimum area polygon for each cluster and, finally merging the polygons. We implement the algorithm and present the results of experiments by comparing the previous works. We compare the average score obtained by our algorithm and that of the previous methods. The score obtained by an algorithm is the ratio given by the area of the computed polygon using that algorithm divided by the area of the convex hull. © 2022, Politechnica University of Bucharest. All rights reserved.

关键词： approximation algorithms

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Online Spatio-Temporal Learning in Deep Neural Networks

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第11期34卷 8894-8908页

作者： Bohnstingl, Thomas Wozniak, Stanislaw Pantazi, Angeliki Eleftheriou, Evangelos IBM Res Zurich CH-8803 Ruschlikon Switzerland Graz Univ Technol Inst Theoret Comp Sci A-8010 Graz Austria Axelera AI CH-8038 Zurich Switzerland

Biological neural networks are equipped with an inherent capability to continuously adapt through online learning. This aspect remains in stark contrast to learning with error backpropagation through time (BPTT) that involves offline computation of the gradients due to the need to unroll the network through time. Here, we present an alternative online learning algorithm framework for deep recurrent neural networks (RNNs) and spiking neural networks (SNNs), called online spatio-temporal learning (OSTL). It is based on insights from biology and proposes the clear separation of spatial and temporal gradient components. For shallow SNNs, OSTL is gradient equivalent to BPTT enabling for the first time online training of SNNs with BPTT-equivalent gradients. In addition, the proposed formulation unveils a class of SNN architectures trainable online at low time complexity. Moreover, we extend OSTL to a generic form, applicable to a wide range of network architectures, including networks comprising long short-term memory (LSTM) and gated recurrent units (GRUs). We demonstrate the operation of our algorithm framework on various tasks from language modeling to speech recognition and obtain results on par with the BPTT baselines.

关键词： Neurons Biology Training Heuristic algorithms approximation algorithms Biological neural networks Backpropagation Backpropagation backpropagation through time (BPTT) online learning real-time recurrent learning (RTRL) spiking neurons

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Streaming algorithms with Large approximation Factors

arXiv

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arXiv 2022年

作者： Li, Yi Lin, Honghao Woodruff, David P. Zhang, Yuheng School of Physical and Mathematical Sciences Nanyang Technological University Singapore Computer Science Department Carnegie Mellon University United States Zhiyuan College Shanghai Jiao Tong University China

We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor α to be much larger than 1. Such algorithms can use significantly less memory than the usual setting for which α = 1 + ǫ for an ǫ ∈ (0, 1), and are motivated by applications to data-driven algorithm design, among other things. We study large approximations for a number of problems in sketching and streaming, assuming that the underlying n-dimensional vector has all coordinates bounded by M throughout the data stream: 1. For the p norm1, 0 Θ(1), which holds even for randomly ordered streams or for streams in the bounded deletion model. Our lower bound also holds for a large class of statistical M -estimators. We also give a 2-pass algorithm that uses less space than the best existing 1-pass algorithm when the entries of the vector are small. 2. For estimating the p norm, p > 2, we show an upper bound of O(n1−2/p(log n log M)/α2) bits for an α-approximation, and give a matching lower bound, for almost the full range of α ≥ 1 for linear sketches. We use this to design algorithms with large approximation factors for cascaded norms and rectangle p norms. 3. For the 2-heavy hitters problem, we show that the known lower bound of Ω(k log n log M) bits for identifying (1/k)-heavy hitters holds even if we are allowed to output items that are 1/(αk)-heavy, for almost the full range of α, provided the algorithm succeeds with probability 1 − O(1/n). We also obtain a lower bound for linear sketches that is tight even for constant probability algorithms. 4. For estimating the number 0 of distinct elements, we give an n1/t-approximation algorithm using O(t log log M) bits of space, as well as a lower bound of Ω(t) bits, both excluding the storage of random bits, where n is the dimension of the underlying frequency vector and M is an upper bound on the magnitude of its coordinates. We also show a separation between 1 and 2 passes

关键词： approximation algorithms

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Variance-Based Exploration for Learning Model Predictive Control

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IEEE ACCESS 2023年 11卷 60724-60736页

作者： Seel, Katrine Bemporad, Alberto Gros, Sebastien Gravdahl, Jan Tommy Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet N-7034 Trondheim Norway SINTEF Digital Dept Math & Cybernet N-0373 Oslo Norway IMT Sch Adv Studies I-55100 Lucca Italy

The combination of model predictive control (MPC) and learning methods has been gaining increasing attention as a tool to control systems that may be difficult to model. Using MPC as a function approximator in reinforcement learning (RL) is one approach to reduce the reliance on accurate models. RL is dependent on exploration to learn, and currently, simple heuristics based on random perturbations are most common. This paper considers variance-based exploration in RL geared towards using MPC as function approximator. We propose to use a non-probabilistic measure of uncertainty of the value function approximator in value-based RL methods. Uncertainty is measured by a variance estimate based on inverse distance weighting (IDW). The IDW framework is computationally cheap to evaluate and therefore well-suited in an online setting, using already sampled state transitions and rewards. The gradient of the variance estimate is then used to perturb the policy parameters in a direction where the variance of the value function estimate is increasing. The proposed method is verified on two simulation examples, considering both linear and nonlinear system dynamics, and compared to standard exploration methods using random perturbations.

关键词： Perturbation methods Uncertainty Predictive models Costs approximation algorithms Predictive control Behavioral sciences Inverse distance weighting model predictive control Q-learning reinforcement learning

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