Assume that we have a random set $\mathcal A$ which is constructed by selecting elements from $U = \{ X_1, \dots, X_n \}$ where $X_i$ are independent samples (concentrated around their expectations $\mathbb E[X_i]$), according to some rule $\kappa$. Let $A$ be the set constructed by applying the rule $\kappa$ to the set $W = \{ \mathbb E[X_1], \dots, \mathbb E[X_n] \}$. I want to ask if there are such problems in probability/learning theory literature and whether there are concentration (or anti-concentration) bounds for them. More specifically I am interested in bounds that bound the following event

$$\Pr[ |A \ominus \mathcal A| \ge t]$$  

where $A \ominus \mathcal A = (A \setminus \mathcal A) \cup (\mathcal A \setminus A)$ (i.e. the symmetric difference between $A$ and $\mathcal A$) and $t \in \mathbb N - \{ 0 \}$.

Intuitively I want to find references where the "expected set" $A$ is "close" (or not) to the actual set $\mathcal A$.