  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.
