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Multiplayer Stackelberg-Nash Game for Nonlinear System via Value Iteration-Based Integral Reinforcement Learning

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022年第4期33卷 1429-1440页

作者： Li, Man Qin, Jiahu Freris, Nikolaos M. Ho, Daniel W. C. Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China Univ Sci & Technol China Sch Comp Sci & Technol Hefei 230027 Peoples R China City Univ Hong Kong Dept Math Hong Kong Peoples R China

In this article, we study a multiplayer Stackelberg-Nash game (SNG) pertaining to a nonlinear dynamical system, including one leader and multiple followers. At the higher level, the leader makes its decision preferentially with consideration of the reaction functions of all followers, while, at the lower level, each of the followers reacts optimally to the leader's strategy simultaneously by playing a Nash game. First, the optimal strategies for the leader and the followers are derived from down to the top, and these strategies are further shown to constitute the Stackelberg-Nash equilibrium points. Subsequently, to overcome the difficulty in calculating the equilibrium points analytically, we develop a novel two-level value iteration-based integral reinforcement learning (VI-IRL) algorithm that relies only upon partial information of system dynamics. We establish that the proposed method converges asymptotically to the equilibrium strategies under the weak coupling conditions. Moreover, we introduce effective termination criteria to guarantee the admissibility of the policy (strategy) profile obtained from a finite number of iterations of the proposed algorithm. In the implementation of our scheme, we employ neural networks (NNs) to approximate the value functions and invoke the least-squares methods to update the involved weights. Finally, the effectiveness of the developed algorithm is verified by two simulation examples.

关键词： Games Heuristic algorithms Mathematical model approximation algorithms Decision making System dynamics Nonlinear dynamical systems Integral reinforcement learning (IRL) multiplayer Stackelberg-Nash game (SNG) neural networks (NNs) nonlinear system value iteration (VI)

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Design of Distributed Event-Triggered Average Tracking algorithms for Homogeneous and Heterogeneous Multiagent Systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第3期67卷 1269-1284页

作者： Zhao, Yu Xian, Chengxin Wen, Guanghui Huang, Panfeng Ren, Wei Northwestern Polytech Univ Sch Automat Xian 710129 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Univ Calif Riverside Dept Elect & Comp Engn Riverside CA 92521 USA

This article addresses the design problem of distributed event-triggered average tracking (DETAT) algorithms for homogeneous and heterogeneous multiagent systems. The objective of the DETAT problem is to develop a group of distributed cooperative control algorithms with event-triggered strategies for agents to track the average of multiple time-varying reference signals. First, for homogeneous linear multiagent systems, based on sampling measurements and model-relied holding techniques, a class of static-gain DETAT algorithms is proposed with a couple of local event-triggered functions for estimators and controllers, respectively. Compared with the existing distributed average tracking (DAT) algorithms, the static-gain DETAT algorithms greatly reduce the cost over communication networks and the frequency of control protocol updates. Second, to reduce the chattering phenomenon caused by nonsmooth items in static-gain algorithms and requirements of the global information of networks, smooth dynamic-gain DETAT algorithms are introduced based on boundary layer approximation methods and self-adaptive principles. Third, for heterogeneous linear multiagent systems, a new algorithm is established by using the output regulation techniques for the heterogeneous DETAT problem. The outputs of heterogeneous agents can ultimately track the average of multiple time-varying reference signals. To the best of our knowledge, it is the first time to study the DETAT problem for heterogeneous multiagent systems. Finally, some examples are presented to show the validity of theoretical results.

关键词： Heuristic algorithms Multi-agent systems Eigenvalues and eigenfunctions approximation algorithms Communication networks Trajectory Regulation Distributed average tracking (DAT) event-triggered strategy homogeneous and heterogeneous dynamics linear multiagent system

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Region-Restricted Sensor Placement Based on Gaussian Process for Sound Field Estimation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2022年 70卷 1718-1733页

作者： Nishida, Tomoya Ueno, Natsuki Koyama, Shoichi Saruwatari, Hiroshi Univ Tokyo Grad Sch Informat Sci & Technol Tokyo 1138656 Japan Tokyo Metropolitan Univ Grad Sch Syst Design Tokyo 1910065 Japan

Sensor placement methods for field estimation based on Gaussian processes are proposed. Generally, sensor placement methods determine the appropriate placement positions by selecting them from predefined candidate positions. Many criteria for the selection have been proposed, with which the quality of the placements is evaluated with regard to the field at the candidate positions. This means that these sensor placement methods seek to find the positions that can estimate the field at the candidate positions accurately. In practical situations, however, the candidate sensor placement region can be different from the target region for field estimation. In this paper, to make sensor placement methods applicable to this situation, we propose two sensor placement methods based on the mean squared error and on conditional entropy that can be applied to cases in which the sensor placement region is arbitrarily restricted. After formulating the sensor placement problems, two approximate algorithms are derived: the greedy algorithm and the convex-relaxation-based algorithm. The application of the proposed methods to sound field estimation is also illustrated, and their effectiveness was confirmed through numerical experiments.

关键词： Estimation Sensor placement Cost function Covariance matrices approximation algorithms Greedy algorithms Gaussian distribution Sensor placement sound field estimation Gaussian process greedy algorithms convex optimization

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Minimizing the Longest Tour Time Among a Fleet of UAVs for Disaster Area Surveillance

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IEEE TRANSACTIONS ON MOBILE COMPUTING 2022年第7期21卷 2451-2465页

作者： Guo, Qing Peng, Jian Xu, Wenzheng Liang, Weifa Jia, Xiaohua Xu, Zichuan Yang, Yanbin Wang, Minghui Sichuan Univ Coll Comp Sci Chengdu 610065 Peoples R China Australian Natl Univ Res Sch Comp Sci Canberra ACT 2601 Australia City Univ Hong Kong Dept Comp Sci Kowloon 83 Tat Chee Ave Hong Kong Peoples R China Dalian Univ Technol Sch Software Dalian 116024 Peoples R China

In this paper, we study the employment of multiple Unmanned Aerial Vehicles (UAVs) to monitor Points of Interests (Pols) in a disaster area, e.g., collapsed buildings after an earthquake, where the UAVs can take photos and videos for the people trapped at Pols, because such valuable information is imperative to make rescue decisions. Unlike most existing studies that ignored the monitoring time of Pols and simply minimized the longest flying distance among the UAVs, we observe that it takes time to monitor the Pols. Then, it is possible that the flying distance of a UAV in its flying tour may not be too long, the tour however contains many densely-located Pols. Therefore, it will take a very long time for the UAV to monitor the Pols in its tour. In this paper, we first formulate a problem of finding flying tours for K given UAVs to collaboratively monitor Pols in a disaster area, such that the maximum spent time of the K UAVs among their tours is minimized, where the spent time of a UAV in its tour consists of the flying time and the Pol monitoring time. We then propose a novel 51/3-approximation algorithm for the problem, improving the best approximation ratio 6 so far for the problem of minimizing the longest flying distance among the UAVs. In addition, we extend the proposed algorithm to the case that each UAV may not be able to monitor all Pols assigned to it, due to its limited maximum flying time (e.g., 30 minutes), and the UAV must return to its depot to replace its battery. We finally evaluate the performance of the proposed algorithms via simulation environments, and experimental results show that the proposed algorithms are very promising. Especially, the maximum spent times of the K UAVs in their tours by the proposed algorithms are up to 30% shorter than those by existing algorithms. In addition, the empirical approximation ratios of the proposed algorithms are no more than 2.4, which are much smaller than their theoretical approximation ratios that are

关键词： Disaster area monitoring with UAVs flying tour scheduling maximum tour time minimization approximation algorithms

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Robustly Guarding Polygons 40

Robustly Guarding Polygons

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40th International Symposium on Computational Geometry, SoCG 2024

作者： Das, Rathish Filtser, Omrit Katz, Matthew J. Mitchell, Joseph S.B. University of Houston TX United States The Open University of Israel Israel Ben-Gurion University of the Negev Beer-Sheva Israel Stony Brook University NY United States

ISBN: (纸本)9783959773164

We propose precise notions of what it means to guard a domain "robustly", under a variety of models. While approximation algorithms for minimizing the number of (precise) point guards in a polygon is a notoriously challenging area of investigation, we show that imposing various degrees of robustness on the notion of visibility coverage leads to a more tractable (and realistic) problem for which we can provide approximation algorithms with constant factor guarantees. © Rathish Das, Omrit Filtser, Matthew J. Katz, and Joseph S.B. Mitchell.

关键词： approximation algorithms

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Subquadratic Submodular Maximization with a General Matroid Constraint 51

Subquadratic Submodular Maximization with a General Matroid ...

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51st International Colloquium on Automata, Languages, and Programming, ICALP 2024

作者： Kobayashi, Yusuke Terao, Tatsuya Research Institute for Mathematical Sciences Kyoto University Japan

ISBN: (纸本)9783959773225

We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized (1−1/e−ϵ)-approximation algorithm that requires Õϵ(√rn) independence oracle and value oracle queries, where n is the number of elements in the matroid and r ≤ n is the rank of the matroid. This improves upon the previously best algorithm by Buchbinder-Feldman-Schwartz [Mathematics of Operations Research 2017] that requires Õϵ(r2 + √rn) queries. Our algorithm is based on continuous relaxation, as with other submodular maximization algorithms in the literature. To achieve subquadratic query complexity, we develop a new rounding algorithm, which is our main technical contribution. The rounding algorithm takes as input a point represented as a convex combination of t bases of a matroid and rounds it to an integral solution. Our rounding algorithm requires Õ(r3/2t) independence oracle queries, while the previously best rounding algorithm by Chekuri-Vondrák-Zenklusen [FOCS 2010] requires O(r2t) independence oracle queries. A key idea in our rounding algorithm is to use a directed cycle of arbitrary length in an auxiliary graph, while the algorithm of Chekuri-Vondrák-Zenklusen focused on directed cycles of length two. © Yusuke Kobayashi and Tatsuya Terao.

关键词： approximation algorithms

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Successively Pruned Q-Learning: Using Self Q-function to Reduce the Overestimation 23

Successively Pruned Q-Learning: Using Self Q-function to Red...

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23rd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2024

作者： Xue, Zhaolin Zhang, Lihua Dong, Zhiyan Fudan University Shanghai China

It's well-known that the Q-learning algorithm suffers the overestimation owing to using the maximum state-action value as an approximation of the maximum expected state-action value. Double Q-learning and other algorithms have been proposed as efficient solutions to alleviate the overestimation. However, these proposed methods intend to utilize multiple Q-functions to reduce the overestimation and ignore the information of single Q-function. In this paper, 1) we reinterpret the update process of Q-learning, build a more precise model compatible with previous model. 2) We propose a novel and simple method to control the maximum bias by employing the information of single Q-function. 3) Our method not only balances between the overestimation and the underestimation, but also attains the minimum bias under proper hyper-parameters. 4) Moreover, it can be naturally generalized to the discrete control domain and continuous control tasks. We reveal that our algorithms outperform Double DQN and other algorithms on some representative games and some classical off-policy actor-critic algorithms can also gain benefits from our method. © 2024 International Foundation for Autonomous Agents and Multiagent Systems.

关键词： approximation algorithms

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Online Inference for Mixture Model of Streaming Graph Signals With Sparse Excitation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2022年 70卷 6419-6433页

作者： He, Yiran Wai, Hoi-To Chinese Univ Hong Kong Dept SEEM Shatin Hong Kong Peoples R China

This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with excitation driven by a sparse matrix. While the mixture model is motivated from practical scenarios, it presents significant challenges to prior graph learning methods. As a remedy, we consider an inference problem focusing on the node centrality of graphs. We design an expectation-maximization (EM) algorithm with a unique low-rank plus sparse prior derived from low pass signal property. We propose a novel online EM algorithm for inference from streaming data. As an example, we extend the online algorithm to detect if the signals are generated from an abnormal graph. We show that the proposed algorithms converge to a stationary point of the maximum-a-posterior (MAP) problem. Numerical experiments support our analysis.

关键词： Signal processing algorithms Inference algorithms Clustering algorithms Topology Mixture models Data models approximation algorithms Blind centrality inference clustering of graph signals expectation maximization online graph learning

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A Novel Neuroevolutionary Paradigm for Solving Strongly Nonlinear Singular Boundary Value Problems in Physiology

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IEEE ACCESS 2022年 10卷 21979-22002页

作者： Guo, Jiayi Khan, Adnan Sulaiman, Muhammad Kumam, Poom Nanjing Univ Posts & Telecommun Sch Software & Cyberspace Secur Nanjing 210049 Peoples R China Abdul Wali Khan Univ Mardan Dept Math Mardan 23200 Khyber Pakhtunk Pakistan King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math KMUTT Fixed Point Theory & Applicat Res GrpKMUTT Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Ctr Excellence Theoret & Computat Sci TaCS CoE Sci Lab Bldg Bangkok 10140 Thailand China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan

In the present research work, we designed a hybrid stochastic numerical solver to investigate nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions arising in various physical models. In this method, we hybridized Harris Hawks Optimizer with Interior Point Algorithm named HHO-IPA. We construct artificial neural networks (ANNs) model for the problem, and this model is tuned with the proposed scheme. This scheme overcomes the singular behavior of problems. The accuracy and applicability of the method are illustrated by finding absolute errors in the solution. The outcomes are compared with the results present in the literature to demonstrate the effectiveness and robustness of the scheme by considering four different nonlinear singular boundary value problems. Further, the convergence of the scheme is proved by performing computational complexity analysis. Moreover, the graphical overview of statistical analysis is added to our investigation to elaborate further on the scheme's stability, accuracy, and consistency.

关键词： Mathematical models approximation algorithms Convergence Boundary conditions Numerical models Computational complexity Rabbits Harris Hawk's optimizer nonlinearity singular boundary value problems artificial neural networks statistical analysis interior point method ordinary differential equations error estimation heuristics bio-inspired algorithms

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S-DIGing: A Stochastic Gradient Tracking Algorithm for Distributed Optimization

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2022年第1期6卷 53-65页

作者： Li, Huaqing Zheng, Lifeng Wang, Zheng Yan, Yu Feng, Liping Guo, Jing Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligen Chongqing 400715 Peoples R China Xinzhou Teachers Univ Dept Comp Sci Xinzhou 034000 Peoples R China

In this article, we study convex optimization problems where agents of a network cooperatively minimize the global objective function which consists of multiple local objective functions. The intention of this work is to solve large-scale optimization problems where the local objective function is complicated, and numerous. Different from most of the existing works, the local objective function of each agent is presented as the average of finite instantaneous functions. Integrating the gradient tracking algorithm with stochastic averaging gradient technology, a distributed stochastic gradient tracking (termed as S-DIGing) algorithm is proposed. At each time instant, only one randomly selected gradient of an instantaneous function is computed, and applied to approximate the local batch gradient for each agent. Based on a novel primal-dual interpretation of the S-DIGing algorithm, it is shown that the S-DIGing algorithm linearly converges to the global optimal solution when step-size do not exceed an explicit upper bound, and the instantaneous functions are strongly convex with Lipschitz continuous gradients. Numerical experiments are presented to demonstrate the practicability of the S-DIGing algorithm, and correctness of the theoretical results.

关键词： Optimization Convergence Linear programming approximation algorithms Stochastic processes Machine learning algorithms Convex functions Distributed optimization gradient tracking stochastic averaging gradient multi-agent systems linear convergence

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