I'm playing a game where I'm trying to estimate an unknown real number $x$.
An oracle exists that will answer the question of "Is a number $y$ greater than or equal to $x$?", to which the oracle will reply either yes or no. The question may be asked an $t$ number of times.
For example, with an unknown $x=9.5$, the oracle will reply yes to $15$ and no to $9$.
What's the best approach to estimate $x$? It's okay to assume my first guess $y_1$ will always be answered with yes (so I always have some "best" guess available), but now I'm tasked with getting even closer to $x$ with my second guess $y_2$, third guess $y_3$, ..., and last guess $y_t$.
I'm not necessarily looking for a solution to this problem, but at least the established name for it so I may do some research. Concepts like optimization, numerical analysis, and machine learning come to mind, but they are large, deep fields, and I'm not quite sure where to turn.
My use case for this algorithm is to discover the optimal frequency to send requests to a service which is frequency-capped by an unknown amount. When I send too fast, I get error responses (oracle says no), and when I'm below the cap, I get success responses (oracle says yes). To keep things focused on the important concept, assume the network has no delay.