Consider an unknown function $f(x,y)$, where $x$ and $y$ are just two scalar numbers in $[0,1]$. $f(x,y)$ is an increasing function of $y$ and is between $0$ and $1$ but is unknown.
At each time I pick a value $y$ and process a value in a stream of $x$ numbers $x_i$, $i=1, 2, ...$ and need to find the minimum $y$ such that $f(x,y)>0.8$.
Is there any principled way to optimize the choices of $y$ assuming $x_i$s does not change fast?
It may be related more to the control theory, but I thought a solution similar to binary search may work:
Increase $y$ if $f(x,y)<0.8$ and decrease it if $f(x,y)>0.8$ using a step size. Now to ensure fast convergence double the step size if $f(A,B)$ does not change status and halve it if it passes $0.8$. The difference with one-sided binary search is that binary search will always halve the step after it passes the bound once, but here we don't do that as the $x$ values might change.