Stochastic Estimation of the Maximum of a Regression Function

1952/09/01 by J. Kiefer, J. Wolfowitz · 114 citations
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification

paper · pdf · doi:10.1214/aoms/1177729392

Abstract

Let M(x) be a regression function which has a maximum at the unknown point θ. M(x) is itself unknown to the statistician who, however, can take observations at any level x. This paper gives a scheme whereby, starting from an arbitrary point x₁, one obtains successively x₂, x₃, ⋯ such that x_n converges to θ in probability as n → ∞.

Citations

• A Stochastic Approximation Method

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