A Stochastic Approximation Method

Robbins, Herbert; Monro, Sutton

doi:10.1007/978-1-4612-5110-1_9

Cited by 676 publications

(831 citation statements)

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“…The only requirement for the psychometric function is monotonicity. Most of these methods could probably be considered as being special cases of stochastic approximation methods (Robbins & Monro, 1951;Blum, 1954;Kesten, 1958;see below).…”

Section: Nonparametric Methodsmentioning

confidence: 99%

“…Most of the reasoning of modified binary search (MOBS) as applied to psychometric functions, i.e. taking into account the probabilistic nature of the subjects' responses, is heuristic and lacks a theoretical foundation, t Robbins and Monro (1951) have shown that for any value of qb between 0 and 1 the sequence given by xo+~ = xn -c (zn -4)) (15) n converges to 0 = x~, with probability 1. Here, c is a suitably chosen constant.…”

Section: Modified Binary Searchmentioning

confidence: 99%

“…An important restriction of the truncated staircase method is that it converges only to the target probability 4> = 0.5. In a forced choice experiment or any other setup, where this target probability is unsuitable, one of the following methods should be used: transformed updown methods (Levitt, 1970), non-parametric up-and-down experimentation (Derman, 1957), the weighted up-down method (Kaernbach, 1991), or stochastic approximation (Robbins & Monro, 1951).…”

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confidence: 99%

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Adaptive psychophysical procedures

1995

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Section: Nonparametric Methodsmentioning

confidence: 99%

Section: Modified Binary Searchmentioning

confidence: 99%

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confidence: 99%

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Adaptive psychophysical procedures

1995

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“…Theorems dealing with the convergence of stochastic algorithms in such form have appeared in the literature see, for example, [21], [11], [28], [29], [30], [31]. These theorems give conditions for a.s. convergence of {ρ n } to some ρ * , where h(ρ * ) = 0.…”

Section: Convergence Analysismentioning

confidence: 99%

“…While the area of stochastic optimization over continuous decision spaces is rich and usually involves gradient-based techniques as in several well-known stochastic approximation algorithms [10], [11], the literature in the area of discrete stochastic optimization is relatively limited. Most known approaches are based on some form of random search, with the added difficulty of having to estimate the cost function at every step.…”

Section: Introductionmentioning

confidence: 99%

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Gokbayrak

Cassandras

2001

Journal of Optimization Theory and Applications

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We consider stochastic discrete optimization problems where the decision variables are non-negative integers. We propose and analyze an on-line control scheme which transforms the problem into a "surrogate" continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both actual and surrogate system states. It is shown that the solution of the original problem is recovered as an element of the discrete state neighborhood of the optimal surrogate state. For the special case of separable cost functions, we show that this methodology becomes particularly efficient. Finally, convergence of the proposed algorithm is established under standard technical conditions and numerical results are included in the paper to illustrate the fast convergence properties of this approach.

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Optimization in simulation: Current issues and the future outlook

Safizadeh

1990

Naval Research Logistics

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Simulation is commonly used to find the best values of decision variables for problems which defy analytical solutions. This objective is similar to that of optimization problems and thus, mathematical programming techniques may be applied to simulation. However, the application of mathematical programming techniques, e.g., the gradient methods, to simulation is compounded by the random nature of simulation responses and by the complexity of the statistical issues involved. The literature relevant to optimization in simulation is scattered, and no comprehensive and up‐to‐date treatment of the subject is presently available. To that end, this article brings together numerous concepts related to t he problem of optimization in simulation. Specifically, it discusses the application of mathematical programming techniques to optimization in simulation, response surface methodology and designs, perturbation analysis, and frequency domain simulation experiments. The article provides a user with an overview of the available optimization techniues and identifies future research possibilities.

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A Stochastic Approximation Method

Cited by 676 publications

References 0 publications

Adaptive psychophysical procedures

Adaptive psychophysical procedures

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Optimization in simulation: Current issues and the future outlook

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