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About 10,000 papers for “Stochastic approximation”

Stochastic approximation. /

Derman, Cyrus, author., Columbia University., United States. Air Force. Office of Scientific Research. · The Journal of the Abraham Lincoln Association

Research supported in part by the Office of Scientific Research of the Air Force, Contract AF 18(600)-442, Project R-345-20-7.

Cited by 0Open access

Stochastic approximation methods

Václav Fabian · Czechoslovak Mathematical Journal · 1960

Some modifications of known approximation procedures are con sidered and general theorems are proved, which make possible the study of their convergence.

Cited by 58Open access

9 Stochastic Approximation

R.L. Kashyap, C.C. Blaydon, Kewei Fu · Mathematics in Science and Engineering/Mathematics in science and engineering · 1970

Cited by 77

On stochastic approximation

Mukerjee, Hari G. · The Open Repository - Binghamton (Binghamton University) · 1976

In many statistical experiments one wishes to obtain a desirable “level of response” corresponding to some “level of treatment.” The response to a given treatment, however, is usually random, and the best one hopes for is to locate the level of treatment that produces the desired response on the average. The mathematical formulation of the problem is as follows. For every level of treatment x, which we assume to be numerical and refer to as an “observation point,” the response (“observation”) y at x is a random variable on some probability space with distribution function Fx and mean m(x) < ∞. Thus m defines a regression function. One wishes to locate a point θ such that m(θ) = α1, where α1 is the desired level of response. A stochastic approximation is a sequential estimation procedure where future observation points are determined on the basis of past information. The two most-discussed procedures for the problem described are the Robbins-Monro (R-M) procedure and the up-and-down method of Dixon and Mood.

Cited by 0

On stochastic approximation /

Dvoretsky, Aryeh, author., Universi©øtah ha-℗ʻIvrit bi-Yerushalayim., Columbia University. et al. · The Journal of the Abraham Lincoln Association

Cited by 0Open access

Quasi stochastic approximation

Darshan Shirodkar, Sean Meyn · 2011

In recent work it was shown that a deterministic analog of stochastic approximation can be formulated to obtain a Q-learning algorithm for approximate optimal control of deterministic and stochastic systems. This paper provides a general foundation for "quasi-stochastic approximation" in which all of the processes under consideration are deterministic, much like quasi-Monte-Carlo for variance reduction in simulation. Applications to root finding and to TD-learning are described, and numerical results are presented.

Cited by 13

ON STOCHASTIC APPROXIMATION

Hans Wolff · ETS Research Bulletin Series · 1970

ABSTRACT This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro [1]. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic mean).

Cited by 1Open access

Stopping Stochastic Approximation

David Hutchison, James C. Spall · 2003

The practical application of stochastic approximation methods require a reliable means to stop the iterative process when the estimate is close to the optimal value or when further improvement of the estimate is doubtful. Conventional ideas on stopping stochastic algorithms employ probabilistic criteria based on the asymptotic distribution of the stochastic approximation process, often with the parameters of the distribution determined by sequential estimation. Difficulties may arise when this approach is applied to small (finite) samples. We propose a different approach that uses the notion of an idealized process as a companion to the stochastic approximation. A discussion of this approach to stopping stochastic approximation is offered in the context of a simple example, including some empirical results.

Cited by 0

Stochastic Approximation Procedure

2020

This chapter discusses jumping stochastic approximation procedure in a Markov environment under the averaging scheme. It illustrates the conditional expectation of a two-component Markov process. The chapter describes the jumping stochastic approximation procedure under diffusion approximating scheme and shows that the investigation of the stochastic approximation procedure in a random Markov environment requires a statistical analysis of the Markov environment. It investigates the convergence of jumping stochastic approximation procedure in a semi-Markov environment using the asymptotic properties of the compensating operator for the extended Markov renewal process and solving its singular perturbation problem. The chapter also considers the asymptotic normality of a continuous procedure of stochastic approximation in the case where the regression function contains a singularly perturbed term depending on the external medium described by a uniformly ergodic Markov process.

Cited by 0

Stochastic approximation methods in stochastic optimization

I. M. Bobylev · Doria (University of Helsinki) · 2013

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

Cited by 0