Speed Predictions for Online Energy-Efficient Scheduling

We consider the scheduling problem of online speed scaling where the goal is to minimize the energy consumption of a machine that controls the speed at which jobs are processed. Recent work has leveraged the learning-augmented framework, where the algorithm is provided with predictions about jobs that will arrive in the future, to manage power usage more efficiently. This paper proposes a novel prediction model for speed scaling where the predictions are about the machine speed (the output), instead of the jobs (the input). Machine speed predictions have multiple advantages: they are succinct, admit strong PAC-learnability guarantees, can be provided dynamically, and lead to a natural definition of smoothness. We give an algorithm for dynamic machine speed predictions that is $(1+\epsilon)$-consistent and $O(1)$-robust. For offline machine speed predictions and job speed predictions, we provide an algorithm that achieves the stronger guarantee of $(1+\epsilon)$-smoothness, while maintaining $O(1)$-robustness. These guarantees are comparable to previous work, but do not require predicting the entire input.