  We study the online problem of minimizing power consumption in systems with
multiple power-saving states. During idle periods of unknown lengths, an
algorithm has to choose between power-saving states of different energy
consumption and wake-up costs. We develop a learning-augmented online algorithm
that makes decisions based on (potentially inaccurate) predicted lengths of the
idle periods. The algorithm's performance is near-optimal when predictions are
accurate and degrades gracefully with increasing prediction error, with a
worst-case guarantee almost identical to the optimal classical online algorithm
for the problem. A key ingredient in our approach is a new algorithm for the
online ski rental problem in the learning augmented setting with tight
dependence on the prediction error. We support our theoretical findings with
experiments.
