Greedy k-Center from Noisy Distance Samples

We study a variant of the canonical $k$-center problem over set vertices in metric space, where underlying distances are apriori unknown. Instead, we can query an oracle which provides noisy/incomplete estimates distance between any pair vertices. consider two models: xmlns:xlink="http://www.w3.org/1999/xlink">Dimension Sampling each to returns points one dimension; and xmlns:xlink="http://www.w3.org/1999/xlink">Noisy Distance true corrupted by noise. propose active algorithms, based on ideas such as UCB, Thompson Sampling Track-and-Stop developed closely related Multi-Armed Bandit problem, adaptively decide queries send able solve $k$ -center problem within approximation ratio with high probability. analytically characterize instance-dependent complexity our algorithms also demonstrate significant improvements naive implementations via numerical evaluations real-world datasets (Tiny ImageNet UT Zappos50 K).