%AEbrahimnejad, Farzam%ALee, James%ABraverman, Mark Ed.%D2022%ISchloss Dagstuhl – Leibniz-Zentrum für Informatik
%KMetrical task systems; online algorithms; metric embeddings; convex optimization; Theory of computation → Online algorithms; Theory of computation → Mathematical optimization; Theory of computation → Random projections and metric embeddings
%MOSTI ID: 10483029
%PMedium: X
%TLeibniz International Proceedings in Informatics (LIPIcs):13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
%XWe present an O((log n)²)-competitive algorithm for metrical task systems (MTS) on any n-point metric space that is also 1-competitive for service costs. This matches the competitive ratio achieved by Bubeck, Cohen, Lee, and Lee (2019) and the refined competitive ratios obtained by Coester and Lee (2019). Those algorithms work by first randomly embedding the metric space into an ultrametric and then solving MTS there. In contrast, our algorithm is cast as regularized gradient descent where the regularizer is a multiscale metric entropy defined directly on the metric space. This answers an open question of Bubeck (Highlights of Algorithms, 2019).
Country unknown/Code not availablehttps://doi.org/10.4230/LIPIcs.ITCS.2022.60OSTI-MSA