Equivalence between the notation and formulations in the introduction and chapters

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The introduction states that "stochastic approximation algorithms deal with"  . The subsequent chapters consider a deterministic function   and a random function  . I have several issues with that. First, one might wonder whether   and  , and what happens to  . Second, the notation   (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   with   or vice versa, please do. I would do it myself, if I were an expert in this matter. AVM2019 (talk) 22:39, 6 April 2021 (UTC)Reply