Sutton Monro (source code)

= Sutton Monro
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<Sutton Monro> coauthored the 1951 <stochastic approximation> paper with <Herbert Robbins>. The original title page verifies both full names and their joint contribution.<A Stochastic Approximation Method by Herbert Robbins and Sutton Monro>[Title page and summary]{ref}

The problem is to find where an unknown mean response $M(x)$ reaches a target $\alpha$ when only noisy observations are available. An update $x_{n+1}=x_n-a_n(Y_n-\alpha)$ moves according to the observed error. Positive step sizes with $\sum a_n=\infty$ and $\sum a_n^2<\infty$, together with suitable response and noise hypotheses, balance continued movement against accumulated noise. The method replaces exact root evaluation by a convergent statistical procedure.<A Stochastic Approximation Method by Herbert Robbins and Sutton Monro>[Sections 1–3]{ref}