Stochastic approximation: Difference between revisions

Revision as of 23:41, 6 June 2011

Revision as of 23:42, 6 June 2011

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* <math>N(x)</math> is uniformly bounded,

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

* <math>M'(x_0\theta)</math> exists and is positive, and

* <math>a_n</math> satisfies the following requirements:

:<math>x_\sum^{n+1\infty}_{i=0}a_i =x_n+a_n( \alpha-N(x_n))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.