Talk:Stochastic approximation

Equivalence between the notation and formulations in the introduction and chapters
The introduction states that "stochastic approximation algorithms deal with" $ f(\theta) = \operatorname E_{\xi} [F(\theta,\xi)] $. The subsequent chapters consider a deterministic function $M(\theta)$ and a random function $N(\theta)$. I have several issues with that. First, one might wonder whether $f(\theta) \equiv M(\theta)$ and $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 $ f(\theta), F(\theta,\xi)$ with $ 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)