Mixing predictions for online metric algorithms

• URL: http://arxiv.org/abs/2304.01781v2
• Date: Fri, 15 Dec 2023 20:24:55 GMT
• Title: Mixing predictions for online metric algorithms
• Authors: Antonios Antoniadis and Christian Coester and Marek Eli\'a\v{s} and Adam Polak and Bertrand Simon
• Abstract summary: We design algorithms that combine predictions and are competitive against such dynamic combinations. Our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the $k$-server problem.
• Score: 34.849039387367455
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of $\ell$ predictors, we obtain a competitive ratio of $O(\ell^2)$, and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a $(1+\epsilon)$-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the $k$-server problem.

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