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- W4313295588 abstract "We show that on every $n$-point HST metric, there is a randomized online algorithm for metrical task systems (MTS) that is $1$-competitive for service costs and $O(log n)$-competitive for movement costs. In general, these refined guarantees are optimal up to the implicit constant. While an $O(log n)$-competitive algorithm for MTS on HST metrics was developed by Bubeck et al. (SODA'19), that approach could only establish an $O((log n)^2)$-competitive ratio when the service costs are required to be $O(1)$-competitive. Our algorithm can be viewed as an instantiation of online mirror descent with the regularizer derived from a multiscale conditional entropy. In fact, our algorithm satisfies a set of even more refined guarantees; we are able to exploit this property to combine it with known random embedding theorems and obtain, for any $n$-point metric space, a randomized algorithm that is $1$-competitive for service costs and $O((log n)^2)$-competitive for movement costs. ----------------- An extended abstract of this paper appeared in the Proceedings of the 32nd Ann. Conference on Learning Theory (COLT 2019)." @default.
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- W4313295588 date "2022-01-01" @default.
- W4313295588 modified "2023-09-30" @default.
- W4313295588 doi "https://doi.org/10.4086/toc.2022.v018a023" @default.
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