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arXiv · 1903.03693

Active Learning a Convex Body in Low Dimensions

Sariel Har-Peled·Mitchell Jones·Saladi Rahul
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Abstract

Consider a set $P \subseteq \Re^d$ of $n$ points, and a convex body $C$ provided via a separation oracle. The task at hand is to decide for each point of $P$ if it is in $C$ using the fewest number of oracle queries. We show that one can solve this problem in two and three dimensions using $O( h(P) \log n)$ queries, where $h(P)$ is the largest subset of points of $P$ in convex position. Furthermore, we show that in two dimensions one can solve this problem using $O( v(P,C) \log^2 n )$ oracle queries, where $v(P, C)$ is a lower bound on the minimum number of queries that any algorithm for this specific instance requires.

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Sariel Har-Peled, Mitchell Jones, Saladi Rahul. 2019-03-08. Active Learning a Convex Body in Low Dimensions. https://arxiv.org/abs/1903.03693

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