Metrical task systems on trees via mirror descent and unfair gluing

@article{Bubeck2019MetricalTS,
  title={Metrical task systems on trees via mirror descent and unfair gluing},
  author={S{\'e}bastien Bubeck and M. B. Cohen and J. Lee and Y. Lee},
  journal={ArXiv},
  year={2019},
  volume={abs/1807.04404}
}
We consider metrical task systems on tree metrics, and present an $O(\mathrm{depth} \times \log n)$-competitive randomized algorithm based on the mirror descent framework introduced in our prior work on the $k$-server problem. For the special case of hierarchically separated trees (HSTs), we use mirror descent to refine the standard approach based on gluing unfair metrical task systems. This yields an $O(\log n)$-competitive algorithm for HSTs, thus removing an extraneous $\log\log n$ in the… Expand
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