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== Equivalence between the notation and formulations in the introduction and chapters ==
The introduction states that "stochastic approximation algorithms deal with" <math display="inline"> f(\theta) = \operatorname E_{\xi} [F(\theta,\xi)] </math>. The subsequent chapters consider a deterministic function <math display="inline">M(\theta)</math> and a random function <math display="inline">N(\theta)</math>. I have several issues with that. First, one might wonder whether <math display="inline">f(\theta) \equiv M(\theta)</math> and <math display="inline">N(\theta) \equiv F(\theta,\xi) </math>, and what happens to <math>\xi</math>. Second, the notation <math>\operatorname E_{\xi} [\dots]</math> (although can be understood as an integral operator) is often criticised, as there is not such thing as "expectation with respect to a variable"; there is just expectation or conditional expectation. Third, even if the previous issues are not issues at all, introducing single-use notation should be avoided (or justified). If someone sees a good way of replacing <math display="inline"> f(\theta), F(\theta,\xi)</math> with <math display="inline"> M(\theta), N(\theta)</math> or vice versa, '''please do'''. I would do it myself, if I were an expert in this matter. [[User:AVM2019|AVM2019]] ([[User talk:AVM2019|talk]]) 22:39, 6 April 2021 (UTC)
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