Online Optimization with Predictions and Non-convex Losses

Abstract

Smoothed online optimization considers an online learning setting where the learner, besides a per-round hitting cost, also incurs a switching cost when changing its decision between rounds. It has received significant attention recently due to its close connections with applications in control and resource allocation. A line of work in this area seeks to design online algorithms that achieve near-optimal costs by leveraging predictions of future cost functions. However, optimistic results are only known under some specific combination of assumptions about the hitting and switching costs, and no general results are known. In this work, we provide two general sufficient conditions that specify a relationship between the hitting and movement costs, which guarantees that a new algorithm, Synchronized Fixed Horizon Control (SFHC), achieves a near-optimal competitive ratio with the help of predictions. The two conditions we give are general because they do not require the cost function to be convex, and natural counterexamples might arise when they are not satisfied.