  We study the fundamental online $k$-server problem in a learning-augmented
setting. While in the traditional online model, an algorithm has no information
about the request sequence, we assume that there is given some advice (e.g.
machine-learned predictions) on an algorithm's decision. There is, however, no
guarantee on the quality of the prediction and it might be far from being
correct.
  Our main result is a learning-augmented variation of the well-known Double
Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in
which we integrate predictions as well as our trust into their quality. We give
an error-dependent competitive ratio, which is a function of a user-defined
trustiness parameter, and which interpolates smoothly between an optimal
consistency, the performance in case that all predictions are correct, and the
best-possible robustness regardless of the prediction quality. When given good
predictions, we improve upon known lower bounds for online algorithms without
advice. We further show that our algorithm achieves for any k an almost optimal
consistency-robustness tradeoff, within a class of deterministic algorithms
respecting local and memoryless properties. Our algorithm outperforms a
previously proposed (more general) learning-augmented algorithm. It is
remarkable that the previous algorithm heavily exploits memory, whereas our
algorithm is memoryless. Finally, we demonstrate in experiments the
practicability and the superior performance of our algorithm on real-world
data.
