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gradient-based simulation optimization under probability constraints

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第2期212卷 345-351页

作者： Andrieu, Laetitia Cohen, Guy Vazquez-Abad, Felisa J. Univ Paris Est CERMICS Ecole Ponts F-77455 Marne La Vallee 2 France EDF R&D Dep OSIRIS F-92141 Clamart France CUNY Hunter Coll Dept Comp Sci New York NY 10065 USA

We study optimization problems subject to possible fatal failures. The probability of failure should not exceed a given confidence level. The distribution of the failure event is assumed unknown, but it can be generated via simulation or observation of historical data. gradient-based simulation-optimization methods pose the difficulty of the estimation of the gradient of the probability constraint under no knowledge of the distribution. In this work we provide two single-path estimators with bias: a convolution method and a finite difference, and we provide a full analysis of convergence of the Arrow-Hurwicz algorithm, which we use as our solver for optimization. Convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates, and numerical results are included via an example of application in finance. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Probability constraints stochastic gradient algorithm stochastic approximation

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Parameter estimation of fractional-order Hammerstein state space system based on the extended Kalman filter

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2023年第7期37卷 1827-1846页

作者： Bi, Yiqun Ji, Yan Qingdao Univ Sci & Technol Coll Automat & Elect Engn Qingdao Peoples R China Qingdao Univ Sci & Technol Coll Automat & Elect Engn Qingdao 266061 Peoples R China

This paper addresses the combined estimation issues of the parameters and states for fractional-order Hammerstein state space systems with colored noises. An extended state estimator is derived by using the parameter estimates to replace the unknown system parameters in Kalman filter. The hierarchical identification principle is introduced to solve the unknown parameters of measurement noises. By introducing the forgetting factor, an extended Kalman filtering-based hierarchical forgetting factor stochastic gradient algorithm is presented to estimate the unknown states, parameters and fractional-order. A numerical example is respectively presented to demonstrate the feasibility of the proposed identification algorithm. It can be seen that the estimation errors are relatively small, which reflects the proposed algorithms have good identification effect.

关键词： extended Kalman filtering forgetting factor fractional-order system hierarchical identification stochastic gradient algorithm

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stochastic differential equation approximations of generative adversarial network training and its long-run behavior

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JOURNAL OF APPLIED PROBABILITY 2024年第2期61卷 465-489页

作者： Cao, Haoyang Guo, Xin Ecole Polytech Ctr Math Appl Route Saclay F-91128 Palaiseau France Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA

This paper analyzes the training process of generative adversarial networks (GANs) via stochastic differential equations (SDEs). It first establishes SDE approximations for the training of GANs under stochastic gradient algorithms, with precise error bound analysis. It then describes the long-run behavior of GAN training via the invariant measures of its SDE approximations under proper conditions. This work builds a theoretical foundation for GAN training and provides analytical tools to study its evolution and stability.

关键词： Generative adversarial networks stochastic gradient algorithm stochastic differential equation

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Convergence of Recursive Identification for ARMAX Process with Increasing Variances

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Tsinghua Science and Technology 2007年第1期12卷 38-43页

作者：金亚罗贵明 School of Software Tsinghua University

The autoregressive moving average exogenous （ARMAX） model is commonly adopted for describing linear stochastic systems driven by colored noise. The model is a finite mixture with the ARMA component and external inputs. In this paper we focus on a parameter estimate of the ARMAX model. Classical modeling methods are usually based on the assumption that the driven noise in the moving average （MA） part has bounded variances, while in the model considered here the variances of noise may increase by a power of log n. The plant parameters are identified by the recursive stochastic gradient algorithm. The diminishing excitation technique and some results of martingale difference theory are adopted in order to prove the convergence of the identification. Finally, some simulations are given to show the reliability of the theoretical results.

关键词： multidimensional autoregressive moving average exogenous (ARMAX) process increasing variance stochastic gradient algorithm convergence

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Upper bounds for the 0-1 stochastic knapsack problem and a B&B algorithm

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ANNALS OF OPERATIONS RESEARCH 2010年第1期176卷 77-93页

作者： Kosuch, Stefanie Lisser, Abdel Univ Paris 11 Rech Informat Lab F-91405 Orsay France

In this paper we study and solve two different variants of static knapsack problems with random weights: The stochastic knapsack problem with simple recourse as well as the stochastic knapsack problem with probabilistic constraint. Special interest is given to the corresponding continuous problems and three different problem solving methods are presented. The resolution of the continuous problems allows to provide upper bounds in a branch-and-bound framework in order to solve the original problems. Numerical results on a dataset from the literature as well as a set of randomly generated instances are given.

关键词： Static stochastic knapsack problems with random weights Simple recourse Chance constrained Expectation constrained B&B algorithm stochastic gradient algorithm Arrow-Hurwicz SOCP

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Parameter estimation algorithm for d-step time delay systems

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2019年第3-4期32卷 199-203页

作者： Gu, Ya Zhu, Peiyi Li, Xiangli Gu, Jianfei Changshu Inst Technol Sch Elect Engn & Automat Changshu Jiangsu Peoples R China

This article proposes the methods of parameter estimation and state estimation to calculate state space systems with delay. Associating the properties of linear conversion and shift operators, the state space model can be equal to the standard state space model, which can then be converted into the recognition model. The proposed stochastic gradient method is brought to calculate the system and converge to the recursive least squares estimates for state space models. Finally, one example is proposed to certify the theorems of this paper.

关键词： state estimation stochastic gradient algorithm time-delay

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The Value of Collaboration in Convex Machine Learning with Differential Privacy 41

The Value of Collaboration in Convex Machine Learning with D...

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41st IEEE Symposium on Security and Privacy (SP)

作者： Wu, Nan Farokhi, Farhad Smith, David Kaafar, Mohamed Ali Macquarie Univ N Ryde NSW Australia CSIRO Data61 Canberra ACT Australia Univ Melbourne Melbourne Vic 3010 Australia Australian Natl Univ Canberra ACT Australia

ISBN: (数字)9781728134970

ISBN: (纸本)9781728134970

In this paper, we apply machine learning to distributed private data owned by multiple data owners, entities with access to non-overlapping training datasets. We use noisy, differentially-private gradients to minimize the fitness cost of the machine learning model using stochastic gradient descent. We quantify the quality of the trained model, using the fitness cost, as a function of privacy budget and size of the distributed datasets to capture the trade-off between privacy and utility in machine learning. This way, we can predict the outcome of collaboration among privacy-aware data owners prior to executing potentially computationally-expensive machine learning algorithms. Particularly, we show that the difference between the fitness of the trained machine learning model using differentially-private gradient queries and the fitness of the trained machine model in the absence of any privacy concerns is inversely proportional to the size of the training datasets squared and the privacy budget squared. We successfully validate the performance prediction with the actual performance of the proposed privacy-aware learning algorithms, applied to: financial datasets for determining interest rates of loans using regression;and detecting credit card frauds using support vector machines.

关键词： Machine learning Differential privacy stochastic gradient algorithm

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Parameter Estimation for Dual-Rate Sampled Data Systems with Preload Nonlinearities 1

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International Conference on Mechanical Engineering and Technology (ICMET 2011)

作者： Chen Jing Lv Lixing Ding Ruifeng Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China Wuxi Profess Coll Sci & Technol Wuxi 214028 Peoples R China

ISBN: (数字)9783642273292

ISBN: (纸本)9783642273285;9783642273292

In this paper. we propose a novel estimation algorithm for a dual-rate system with preload nonlinearity. The input-output data are measured two different sampling rates. A switching function and a polynomial transformation technique are employed to derive a mathematical model for such a dual-rate and nonlinear system. Furthermore, two modified stochastic gradient algorithms are given to improve the convergence rate. Finally a simulation example is provided to verify the effectiveness of the proposed method.

关键词： Parameter estimation stochastic gradient algorithm Preload nonlinearity Dual-rate system Convergence rate

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Convergence of modified SG algorithm with quantized observations 43

Convergence of modified SG algorithm with quantized observat...

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43rd Chinese Control Conference (CCC)

作者： Yan, Ren Liu, Zhixin Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

ISBN: (纸本)9798350366907;9789887581581

This paper considers the identification problem of linear regression model with quantized observations. We propose a modified stochastic gradient algorithm to estimate unknown parameters using the quanized observations. Under the "weakest" excitation condition, we show that the proposed algorithm converges to the true parameters without requiring the commonly used i.i.d. conditions. Based on this, the convergence rate is further considered. Finally, simulation results are given to demonstrate the effectiveness of the proposed algorithm.

关键词： stochastic gradient algorithm quantized observations convergence rate parameter identification stochastic dynamic system

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Convex Combination of Subband Adaptive Filters for Sparse Impulse Response Systems

Convex Combination of Subband Adaptive Filters for Sparse Im...

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54th IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

作者： Sohn, Sang-Wook Yun, Jae-Jun Lee, Jeongkyu Bae, Hyeon-Deok Choi, Hun Chungbuk Natl Univ Dept Elect Engn Chonju South Korea Dong Eui Univ Dept Elect Engn Busan South Korea

ISBN: (纸本)9781612848570

It is well known, combination scheme is suitable for improving the performance of adaptive algorithms. In this paper, we propose a subband combination scheme for sparse impulse response system. The combination is carried out in subband domain. In this convex combination, SIPNLMS and SNLMS are derived for fast convergence and small steady state error respectively. And mixing parameters are described by minimum mean square error and stochastic gradient algorithm. In adaptive system identification scenario, the advantages of this proposed method are illustrated.

关键词： Filtering SIPNLMS method SNLMS method adaptive algorithm performance adaptive filters adaptive system identification combinatorial mathematics convex combination convex programming gradient methods least mean squares methods minimum mean square error method sparse improve proportionate normalized least mean square method sparse impulse response system sparse normalized least mean square method steady state error stochastic gradient algorithm stochastic processes subband adaptive filter subband combination scheme transient response

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