Efficient Online Learning for Dynamic k-Clustering
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We study dynamic clustering problems from the perspective of online learning. We consider an online learning problem, called Dynamic k-Clustering, in which k centers are maintained in a metric space over time (centers may change positions) such as a dynamically changing set of r clients is served in the best possible way. The connection cost at round t is given by the p-norm of the vector consisting of the distance of each client to its closest center at round t, for some p≥ 1 or p = ∞. We present a Θ( min(k,r) )-regret polynomial-time online learning algorithm and show that, under some well-established computational complexity conjectures, constant-regret cannot be achieved in polynomial-time. In addition to the efficient solution of Dynamic k-Clustering, our work contributes to the long line of research on combinatorial online learning.
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