Chasing convex bodies, from 1817 to 2018

  • Sebastien Bubeck | Microsoft Research Lab - Redmond

A selector maps a set (in some set system) to an element in that set. In a metric space, Lipschitz selection is the problem of finding a selector that is Lipschitz with respect to the Hausdorff distance. A classical result is the existence of a Lipschitz selector for convex sets in Euclidean space. In this talk we will prove an *online* version of this classical result. This resolves the 1991 Friedman-Linial conjecture on convex body chasing.

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