Active-Learning a Convex Body in Low Dimensions

Consider a set $$P\subseteq \mathbb {R}^d$$ of n points, and convex body $$C$$ provided via separation oracle. The task at hand is to decide for each point $$P$$ if it in using the fewest number oracle queries. We show that one can solve this problem two three dimensions queries, where size largest subset points position. In 2D, we provide an algorithm efficiently generates these adaptive Furthermore, lower bound on minimum queries any specific instance requires. Finally, consider other variations problem, such as contains all . As application above, discrete geometric median P $$\mathbb {R}^2$$ be computed expected time.