Mixing predictions for online metric algorithms

Motivated by the power of machine-learned predictions, the field of learningaugmented algorithms has been growing rapidly in recent years. In the classical field of online algorithms, an input sequence is revealed to an algorithm over time and it is assumed that at all times, no information about the future part of the input is available. In contrast, a learning-augmented algorithm additionally has access to predictions (e.g., machine-learned) related to the future input. These predictions may be inaccurate, so a challenge is to simultaneously utilize high-quality predictions to their best advantage while at the same time avoiding to be misled by erroneous predictions. An important technique in the field of learning-augmented algorithms is the method of combining multiple algorithms into a single hybrid algorithm that leverages the advantages of all individual algorithms. The basic idea goes back to several decades before the area of learning-augmented algorithms was born and also has applications, for example, in pure online algorithms: Fiat et al. [1990] defined a MIN operator on algorithms for the k-server problem that combines several algorithms into one whose cost matches the best of them up to