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Here <math>H(\theta, X)</math> is an unbiased estimator of <math>\nabla g(\theta)</math>. If <math>X</math> depends on <math>\theta</math>, there is in general no natural way of generating a random outcome <math>H(\theta, X)</math> that is an unbiased estimator of the gradient. In some special cases when either IPA or likelihood ratio methods are applicable, then one is able to obtain an unbiased gradient estimator <math>H(\theta, X)</math>. If <math>X</math> is viewed as some "fundamental" underlying random process that is generated ''independently'' of <math>\theta</math>, and under some regularization conditions for derivative-integral interchange operations so that <math>\operatorname{E}\Big[\frac{\partial}{\partial\theta}Q(\theta,X)\Big] = \nabla g(\theta)</math>, then <math>H(\theta, X) = \frac{\partial}{\partial \theta}Q(\theta, X)</math> gives the fundamental gradient unbiased estimate. However, for some applications we have to use finite-difference methods in which <math>H(\theta, X)</math> has a conditional expectation close to <math>\nabla g(\theta)</math> but not exactly equal to it.
We then define a recursion analogously to [[Newton's Method]] in the deterministic algorithm:
: <math display="block">\theta_{n+1} = \theta_n - \varepsilon_n H(\theta_n,X_{n+1}).</math>
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