Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing

This paper proposes a new model for augmenting algorithms with useful predictions that go beyond worst-case bounds on the algorithm performance. By refining existing models, our model ensures predictions are formally learnable and instance robust. Learnability guarantees that predictions can be efficiently constructed from past data. Instance robustness formally ensures a prediction is robust to modest changes in the problem input. Further, the robustness model ensures two different predictions can be objectively compared, addressing a shortcoming in prior models. This paper establishes the existence of predictions which satisfy these properties. The paper considers online algorithms with predictions for a network flow allocation problem and the restricted assignment makespan minimization problem. For both problems, three key properties are established: existence of useful predictions that give near optimal solutions, robustness of these predictions to errors that smoothly degrade as the underlying problem instance changes, and we prove high quality predictions can be learned from a small sample of prior instances.