Stochastic approximation: Difference between revisions

Revision as of 23:42, 6 June 2011

Revision as of 23:43, 6 June 2011

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* <math>M(x)</math> is nondecreasing,

* <math>M'(\theta)</math> exists and is positive, and

* <math>a_n</math> satisfies the following requirements: <math>\quad \sum^{\infty}_{i=0}a_i = \infty \quad </math> and <math>\quad \sum^{\infty}_{i=0}a^2_i < \infty \quad </math>

:<math>\sum^{\infty}_{i=0}a_i = \infty</math>

The last condition is fulfilled for example by taking <math>a_n=1/n</math>; other series are possible but in order to average out the noise in <math>N(x)</math>, <math>a_n</math> must converge slowly.