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robbins-monro algorithm with ψ-Mixing Random Errors

MATHEMATICAL METHODS OF STATISTICS 2022年第3期31卷 105-119页

作者： El Moumen, AbdelKader Benslimane, Salim Rahmani, Samir Univ Bejaia Fac Sci Exactes Lab Math Appl Bejaia 06000 Algeria Univ Tamenghasset Tamenghasset 11000 Algeria Engineer Sch Comp Sci & Digital Technol ESTIN Lab Informat & Technol Avancees Numer Bejaia Algeria Univ Bejaia Fac Technol Bejaia 06000 Algeria

In this work, we first establish exponential inequalities for the robbins-monro's algorithm under psi-mixing random errors. Then, we present a numerical application that uses the main result of this work to approx... 详细信息

关键词： robbins-monro algorithm dependence psi-mixing application

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Adaptive designs and robbins-monro algorithm

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2005年第1期131卷 161-174页

作者： Moler, JA Plo, F San Miguel, M Univ Publ Navarra Dept Estad & Invest Operat Pamplona 31006 Spain Univ Zaragoza Fac Ciencias Dept Metodos Estad E-50009 Zaragoza Spain

An adaptive design for a clinical trial with prognostic factors and more than two treatments is described using a generalised urn model in a random environment. The evolution of the urn composition is expressed by a recurrence equation that fits the robbins-monro scheme of stochastic approximation. Then, the Ordinary Differential Equation method is used to obtain strong laws. Besides, central limit theorems are also obtained. These results are useful to make inference about the parameters of the clinical trial. (C) 2003 Elsevier B.V. All rights reserved.

关键词： adaptive designs urn models robbins-monro algorithm ODE method

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A robbins-monro-type algorithm for computing global minimizer of generalized conic functions

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OPTIMIZATION 2015年第9期64卷 1999-2020页

作者： Barczy, Matyas Nagy, Abris Noszaly, Csaba Vincze, Csaba Univ Debrecen Fac Informat Dept Appl Math & Probabil Debrecen Hungary Hungarian Acad Sci Inst Math MTA DE Res Grp Equat Funct & Curves Debrecen Hungary Univ Debrecen Debrecen Hungary Univ Debrecen Inst Math Debrecen Hungary

We generalize the notion and some properties of the conic function introduced by Vincze and Nagy in 2012. We provide a stochastic algorithm for computing the global minimizer of generalized conic functions, we prove a... 详细信息

关键词： global optimization Markov process conic function stochastic algorithm robbins-monro algorithm 90C25 60D05

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Superposed semi-Markov decision process with application to optimal maintenance systems

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2025年第3期49卷 1-19页

作者： Shi, Jianmin Wuhan Univ Sch Math & Stat Wuhan Peoples R China Wuhan Univ Sch Econ & Management Wuhan Peoples R China Res Inst Haitong Secur Shanghai Peoples R China

This paper investigates the superposition problem of two or more individual semi-Markov decision processes (SMDPs). The new sequential decision process superposed by individual SMDPs is no longer an SMDP and cannot be handled by routine iterative algorithms, but we can expand its state spaces to obtain a hybrid-state SMDP. Using this hybrid-state SMDP as an auxiliary and inspired by the robbins-monro algorithm underlying the reinforcement learning method, we propose an iteration algorithm based on a combination of dynamic programming and reinforcement learning to numerically solve the superposed sequential decision problem. As an illustration example, we apply our superposition model and algorithm to solve the optimal maintenance problem of a two-component independent parallel system.

关键词： Superposition Semi-Markov decision process Hybrid state robbins-monro algorithm Maintenance

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A combined direction stochastic approximation algorithm

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OPTIMIZATION LETTERS 2010年第1期4卷 117-129页

作者： Xu, Zi Shanghai Univ Dept Math Coll Sci Shanghai 200444 Peoples R China

The stochastic approximation problem is to find some root or minimum of a nonlinear function in the presence of noisy measurements. The classical algorithm for stochastic approximation problem is the robbins-monro (RM) algorithm, which uses the noisy negative gradient direction as the iterative direction. In order to accelerate the classical RM algorithm, this paper gives a new combined direction stochastic approximation algorithm which employs a weighted combination of the current noisy negative gradient and some former noisy negative gradient as iterative direction. Both the almost sure convergence and the asymptotic rate of convergence of the new algorithm are established. Numerical experiments show that the new algorithm outperforms the classical RM algorithm.

关键词： Stochastic approximation robbins-monro algorithm Combined direction Almost sure Asymptotic rate of convergence

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Optimization of the transient and steady-state behavior of discrete event systems

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MANAGEMENT SCIENCE 1996年第5期42卷 717-737页

作者： Andradottir, S UNIV WISCONSIN DEPT IND ENGN MADISON WI 53706 USA

We present a general framework for applying simulation to optimize the behavior of discrete event systems. Our approach involves modeling the discrete event system under study as a general state space Markov chain whose distribution depends on the decision parameters. We then show how simulation and the likelihood ratio method can be used to evaluate the performance measure of interest and its gradient, and we present conditions that guarantee that the robbins-monro stochastic approximation algorithm will converge almost surely to the optimal values of the decision parameters. Both transient and steady-state performance measures are considered. For steady-state performance measures, we consider both the case when the Markov chain of interest is regenerative in the standard sense, as well as the case when this Markov chain is Harris recurrent, and thereby regenerative in a wider sense.

关键词： stochastic optimization simulation stochastic approximation gradient estimation robbins-monro algorithm regenerative method likelihood ratio method Markov chains Harris recurrence

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A General Framework for Temporal Fair User Scheduling in NOMA Systems

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2019年第3期13卷 408-422页

作者： Shahsavari, Shahram Shirani, Farhad Erkip, Elza NYU Tandon Sch Engn Dept Elect & Comp Engn New York NY 10012 USA

Non-orthogonal multiple access (NOMA) is one of the promising radio access techniques for next generation wireless networks. Opportunistic multi-user scheduling is necessary to fully exploit multiplexing gains in NOMA systems, but compared with traditional scheduling, inter-relations between users' throughputs induced by multi-user interference poses new challenges in the design of NOMA schedulers. A successful NOMA scheduler has to carefully balance the following three objectives: Maximizing average system utility, satisfying desired fairness constraints among the users and enabling real time, and low computational cost implementations. In this paper, scheduling for NOMA systems under temporal fairness constraints is considered. Temporal fair scheduling leads to communication systems with predictable latency as opposed to utilitarian fair schedulers for which latency can be highly variable. It is shown that under temporal fairness constraints, optimal system utility is achieved using a class of opportunistic scheduling schemes called threshold based strategies (TBS). One of the challenges in heterogeneous NOMA scenarios-where only specific users may be activated simultaneously-is to determine the set of feasible temporal shares. A variable elimination algorithm is proposed to accomplish this task. Furthermore, an (online) iterative algorithm based on the robbins-monro method is proposed to construct a TBS by finding the optimal thresholds for a given system utility metric. The algorithm does not require knowledge of the users' channel statistics. Rather, at each time slot, it has access to the channel realizations in the previous time slots. Various numerical simulations of practical scenarios are provided to illustrate the effectiveness of the proposed NOMA scheduling in static and mobile scenarios.

关键词： Non-orthogonal multiple access multi-user scheduling temporal fairness threshold-based strategies robbins-monro algorithm

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CONVERGENCE OF SELF-ORGANIZING NEURAL algorithmS

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NEURAL NETWORKS 1992年第3期5卷 485-493页

作者： YANG, H DILLON, TS La Trobe University Australia

Cottrell-Fort's model and some self-organizing neural algorithms are analyzed in this paper In the one-dimensional case, the almost sure convergence for Cottrell-Fort's algorithm is obtained when the probability distribution of stimulus center is not uniform. A new algorithm is designed which is the combination of Kohonen and Cottrell-Fort's algorithms. In the two-dimensional case, another new training algorithm is provided which is different from Cottrell-Fort's. It also has almost sure convergence for rather general stimulus distributions. An interaction parameter is introduced to make the model more flexible. For any boundary condition, the algorithm is convergent when suitable stimulus distributions are applied. The self-organized map depends on the stimulus distribution and the boundary conditions but not on the initial map. It shows some relation between the statistical distribution of the stimulus and the connection structure in the neural maps. The system is robust and reliable. An example in the one-dimensional case shows that even if some nodes have zero stimulus probability the system can still form an ordered map from an unordered initial map.

关键词： SELF-ORGANIZING NEURAL MAPS ALMOST SURE CONVERGENCE robbins-monro algorithm NONUNIFORM STIMULUS DISTRIBUTION INTERACTION PARAMETER

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On throughput stabilization of network transport

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IEEE COMMUNICATIONS LETTERS 2004年第1期8卷 66-68页

作者： Rao, NSV Wu, QS Iyengar, SS Oak Ridge Natl Lab Div Math & Comp Sci Oak Ridge TN 37831 USA Louisiana State Univ Dept Comp Sci Baton Rouge LA 70803 USA

A number of network applications require stable transport throughput for tasks such as control and coordination operations over wide-area networks. We present a window-based method that achieves stable throughput at a target level by utilizing a variation of the classical robbins-monro stochastic approximation algorithm. We analytically show the stability of this method under very mild conditions on the network, which are justified by Internet measurements. Our User Datagram Protocol (UDP)-based implementation provides stable throughput over the Internet under various traffic conditions.

关键词： robbins-monro algorithm stochastic approximation transport stabilization

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Design weighting parameter tuning of multivariable self-tuning controllers

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COMPUTERS & ELECTRICAL ENGINEERING 2002年第6期28卷 465-480页

作者： Cho, WC Lee, IS Kim, KY Kyongdo Prov Coll Dept Comp Appl Elect Yecheonkun 757800 Kyungsangpook D South Korea Sangju Natl Univ Dept Elect & Elect Engn Sangju City 742711 Kyungsangpook D South Korea Cheju Natl Univ Dept Elect Engn Cheju City 690756 South Korea

In this paper, we present the method for on-line tuning of a design weighting polynomial parameters of a multivariable self-tuning controller which adapts to changes in the higher-order nonminimum phase system parameters with time delays and noises. The algorithm effect is achieved through the recursive least square algorithm at the parameter estimation stage and also through the robbins-monro, algorithm at the stage of optimizing the design weighting polynomial parameters of the controller. The proposed method is simple and effective compared with the pole restriction method. The computer simulation results are presented to adapt the higher-order multivariable system with nonminimum phase and with changeable system parameters. (C) 2002 Published by Elsevier Science Ltd.

关键词： design weighting polynomial parameters multivariable self-tuning controller robbins-monro algorithm higher-order nonminimum phase system pole restriction

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