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

TL;DR

This paper introduces a framework for augmenting online algorithms with learnable and robust predictions, ensuring efficiency, robustness to input changes, and improved performance in network flow and load balancing problems.

Contribution

It develops a formal model for learnable and instance-robust predictions and applies it to online matching, flows, and load balancing, demonstrating their effectiveness.

Findings

High-quality predictions can be learned from limited data.

Predictions degrade smoothly with input changes, maintaining performance.

Algorithms outperform worst-case bounds with robust, learned predictions.

Abstract

We propose a new model for augmenting algorithms with predictions by requiring that they are formally learnable and instance robust. Learnability ensures that predictions can be efficiently constructed from a reasonable amount of past data. Instance robustness ensures that the prediction is robust to modest changes in the problem input, where the measure of the change may be problem specific. Instance robustness insists on a smooth degradation in performance as a function of the change. Ideally, the performance is never worse than worst-case bounds. This also allows predictions to be objectively compared. We design online algorithms with predictions for a network flow allocation problem and restricted assignment makespan minimization. For both problems, two key properties are established: high quality predictions can be learned from a small sample of prior instances and these predictions are robust to errors that smoothly degrade as the underlying problem instance changes.