Talk:Stochastic approximation

Equivalence between the notation and formulations in the introduction and chapters

The introduction states that "stochastic approximation algorithms deal with" ${\textstyle f(\theta )=\operatorname {E} _{\xi }[F(\theta ,\xi )]}$. The subsequent chapters consider a deterministic function ${\textstyle M(\theta )}$ and a random function ${\textstyle N(\theta )}$. I have several issues with that. First, one might wonder whether ${\textstyle f(\theta )\equiv M(\theta )}$ and ${\textstyle N(\theta )\equiv F(\theta ,\xi )}$, and what happens to $\xi$. Second, the notation $\operatorname {E} _{\xi }[\dots ]$ (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 ${\textstyle f(\theta ),F(\theta ,\xi )}$ with ${\textstyle M(\theta ),N(\theta )}$ 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)