On fixed gain recursive estimators with discontinuity in the parameters

ESAIM Probability and Statistics ◽

10.1051/ps/2018019 ◽

2019 ◽

Vol 23 ◽

pp. 217-244

Author(s):

Huy N. Chau ◽

Chaman Kumar ◽

Miklós Rásonyi ◽

Sotirios Sabanis

Keyword(s):

Stochastic Approximation ◽

Approximation Scheme ◽

Tracking Error ◽

Mixing Condition ◽

Underlying Process ◽

Recursive Estimators

In this paper, we estimate the expected tracking error of a fixed gain stochastic approximation scheme. The underlying process is not assumed Markovian, a mixing condition is required instead. Furthermore, the updating function may be discontinuous in the parameter.

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A two Timescale Stochastic Approximation Scheme for Simulation-Based Parametric Optimization

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800005362 ◽

1998 ◽

Vol 12 (4) ◽

pp. 519-531 ◽

Cited By ~ 32

Author(s):

Shalabh Bhatnagar ◽

Vivek S. Borkar

Keyword(s):

Stochastic Approximation ◽

Perturbation Analysis ◽

Parametric Optimization ◽

Approximation Scheme ◽

Infinitesimal Perturbation Analysis ◽

Simulation Based ◽

Infinitesimal Perturbation ◽

Two Timescale Stochastic Approximation

A two timescale stochastic approximation scheme which uses coupled iterations is used for simulation-based parametric optimization as an alternative to traditional “infinitesimal perturbation analysis” schemes. It avoids the aggregation of data present in many other schemes. Its convergence is analyzed, and a queueing example is presented.

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Continuous stochastic approximation with semi-Markov switchings in the diffusion approximation scheme

Cybernetics and Systems Analysis ◽

10.1007/s10559-007-0086-y ◽

2007 ◽

Vol 43 (4) ◽

pp. 605-612 ◽

Cited By ~ 1

Author(s):

Ya. M. Chabanyuk

Keyword(s):

Stochastic Approximation ◽

Diffusion Approximation ◽

Approximation Scheme

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A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities

Proceedings of the 2011 Winter Simulation Conference (WSC) ◽

10.1109/wsc.2011.6148100 ◽

2011 ◽

Cited By ~ 2

Author(s):

Farzad Yousefian ◽

Angelia Nedic ◽

Uday V. Shanbhag

Keyword(s):

Variational Inequalities ◽

Stochastic Approximation ◽

Approximation Scheme ◽

Stochastic Variational Inequalities

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A stochastic approximation scheme and convergence theorem for particle interactions with perfectly reflecting boundary conditions

Monte Carlo Methods and Applications ◽

10.1515/156939606778705182 ◽

2006 ◽

Vol 12 (3) ◽

Cited By ~ 5

Author(s):

C. G. Wells

Keyword(s):

Boundary Conditions ◽

Stochastic Approximation ◽

Convergence Theorem ◽

Approximation Scheme ◽

Particle Interactions

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eg-VSSA: An extragradient variable sample-size stochastic approximation scheme: Error analysis and complexity trade-offs

2016 Winter Simulation Conference (WSC) ◽

10.1109/wsc.2016.7822133 ◽

2016 ◽

Cited By ~ 2

Author(s):

Afrooz Jalilzadeh ◽

Uday V. Shanbhag

Keyword(s):

Error Analysis ◽

Sample Size ◽

Stochastic Approximation ◽

Approximation Scheme ◽

Variable Sample Size ◽

Trade Offs

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Distributed Parameter Identification Using the Method of Characteristics

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3426479 ◽

1971 ◽

Vol 93 (2) ◽

pp. 73-78 ◽

Cited By ~ 16

Author(s):

William T. Carpenter ◽

Michael J. Wozny ◽

Raymond E. Goodson

Keyword(s):

Distributed Systems ◽

Parameter Identification ◽

Stochastic Approximation ◽

Method Of Characteristics ◽

Approximation Scheme ◽

Multidimensional Systems ◽

Distributed Parameter ◽

The Method Of Characteristics ◽

Noisy Measurements ◽

And Diffusion

A method is presented for estimating parameters in distributed systems which can be analyzed by the method of characteristics. Both the very real problems of noisy measurements and limited available measurement transducers are discussed in some depth. Convergent algorithms are developed using a Robbins-Munro stochastic approximation scheme. The extension of these methods to the identification of function multidimensional systems, and diffusion terms is considered.

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Stochastic Recursive Inclusions in Two Timescales with Nonadditive Iterate-Dependent Markov Noise

Mathematics of Operations Research ◽

10.1287/moor.2019.1037 ◽

2020 ◽

Vol 45 (4) ◽

pp. 1405-1444

Author(s):

Vinayaka G. Yaji ◽

Shalabh Bhatnagar

Keyword(s):

Asymptotic Behavior ◽

Markov Chain ◽

Convex Optimization ◽

Objective Function ◽

Recent Work ◽

Differential Inclusion ◽

Stochastic Approximation ◽

Optimization Problem ◽

Approximation Scheme ◽

Convex Optimization Problem

In this paper, we study the asymptotic behavior of a stochastic approximation scheme on two timescales with set-valued drift functions and in the presence of nonadditive iterate-dependent Markov noise. We show that the recursion on each timescale tracks the flow of a differential inclusion obtained by averaging the set-valued drift function in the recursion with respect to a set of measures accounting for both averaging with respect to the stationary distributions of the Markov noise terms and the interdependence between the two recursions on different timescales. The framework studied in this paper builds on a recent work by Ramaswamy and Bhatnagar, by allowing for the presence of nonadditive iterate-dependent Markov noise. As an application, we consider the problem of computing the optimum in a constrained convex optimization problem, where the objective function and the constraints are averaged with respect to the stationary distribution of an underlying Markov chain. Further, the proposed scheme neither requires the differentiability of the objective function nor the knowledge of the averaging measure.

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Bandwidth Selection for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method

Journal of Probability and Statistics ◽

10.1155/2014/739640 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 17

Author(s):

Yousri Slaoui

Keyword(s):

Stochastic Approximation ◽

Estimation Error ◽

Bandwidth Selection ◽

Small Sample ◽

Squared Error ◽

Integrated Squared Error ◽

Theoretical Results ◽

Selection Of ◽

Better Than ◽

Recursive Estimators

We propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. (2009a). We showed that, using the selected bandwidth and the stepsize which minimize the MISE (mean integrated squared error) of the class of the recursive estimators defined in Mokkadem et al. (2009a), the recursive estimator will be better than the nonrecursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study.

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