The use of machine learning and predictive models have produced a revolution in science and engineering. Online optimization problems are a natural source of uncertainty that predictions can be used to manage and improve performance. This paper studies how predictive techniques can be used to break through worst case barriers in online scheduling.
The make-span minimization problem on unrelated machines and its special case, restricted assignment, are classic problems in online scheduling theory. Worst case analysis of these problems yields Ω(log m) lower bounds on the competitive ratio in the online setting. In this paper we construct non-trivial predictions for these problems and design algorithms that utilize these predictions to compute solutions online. Our predictions are compact in size, having dimension linear in the number of machines. The performance guarantees of our algorithms depend on the accuracy of the predictions, and moderately accurate predictions allow our techniques to beat the worst case lower bounds. More precisely, the predictions can be used to construct O(log η)-competitive fractional assignments, where η is the error of the predictions. We then give an online algorithm that is O(poly(log log(m)))-competitive to round these fractional assignments