Stochastic approximation: Difference between revisions

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Robbins–Monro algorithm: example with estimating mean
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Consider the problem of estimating the mean <math>\theta^*</math> of a probability distribution from a stream of independent samples <math>X_1, X_2, \dots</math>.
 
Let <math>N(\theta) := X - \theta</math>, then the unique solution to <math display="inline">\operatorname E[N(\theta)] = 0</math> is the desired mean <math>\theta^*</math>. The RM algorithm gives us<math display="block">\theta_{n+1}=\theta_n - a_n(X_n - \theta_n - \alpha)</math>
 
===Complexity results===