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—Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root finding with noisy input information. As with all stochastic search algorithms , there are adjustable algorithm coefficients that must be specified, and that can have a profound effect on algorithm performance. It is known that choosing these coefficients… (More)

- James C Spall
- 1998

ultivariate stochastic optimization plays a major role in the analysis and control of many engineering systems. In almost all real-world optimization problems, it is necessary to use a mathematical algorithm that iteratively seeks out the solution because an analytical (closed-form) solution is rarely available. In this spirit, the " simultaneous… (More)

—Consider the problem of developing a controller for general (nonlinear and stochastic) systems where the equations governing the system are unknown. Using discrete-time measurements , this paper presents an approach for estimating a controller without building or assuming a model for the system (including such general models as differential/difference… (More)

- James C Spall
- 2005

The Fisher information matrix summarizes the amount of information in the data relative to the quantities of interest. There are many applications of the information matrix in modeling, systems analysis, and estimation, including confidence region calculation, input design, prediction bounds, and " noninformative " priors for Bayesian analysis. This article… (More)

- J C Spall
- 2004

This section provides answers to selected exercises in the chapters and appendices. An asterisk (*) indicates that the solution here is incomplete relative to the information requested in the exercise. Unless indicated otherwise, the answers here are identical to those in the text on pp. 552−557 (it is possible that future versions of this site may include… (More)

The simultaneous perturbation stochastic approximation SPSA algorithm has recently attracted considerable attention for optimization problems where it is diicult or impossible to obtain a direct gradient of the objective say, loss function. The approach is based on a highly eecient simultaneous perturbation approximation to the gradient based on loss… (More)

—It is known that a stochastic approximation (SA) analogue of the deterministic Newton-Raphson algorithm provides an asymptotically optimal or near-optimal form of stochastic search. However, directly determining the required Jacobian matrix (or Hessian matrix for optimization) has often been difficult or impossible in practice. This paper presents a… (More)

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The approach here is based on using the output error of the system to train the NN controller without the need to assume or construct a separate model (NN or other type) for the unknown process dynamics. To implement such a… (More)

- James C Spall, A Sourcebook, Sarah Watstein, Robert Anthony Laurich
- 2010

A unique interdisciplinary foundation for real-world problem solvingStochastic search and optimization techniques are used in a vast number of areas, including aerospace, medicine, transportation, and finance, to name but a few. Whether the goal is refining the design of a missile or aircraft, determining the effectiveness of a new drug, developing the most… (More)