A Regression Approach to Learning-Augmented Online Algorithms
It addresses performance improvement for online algorithms in domains like ski rental and scheduling, but is incremental as it adapts existing regression ideas to a specific framework.
The paper tackles the problem of predicting real-valued parameters for learning-augmented online algorithms using regression, showing nearly tight bounds on sample complexity and extending results to the agnostic setting.
The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a natural approach is to use regression techniques to make these predictions. We introduce this approach in this paper, and explore it in the context of a general online search framework that captures classic problems like (generalized) ski rental, bin packing, minimum makespan scheduling, etc. We show nearly tight bounds on the sample complexity of this regression problem, and extend our results to the agnostic setting. From a technical standpoint, we show that the key is to incorporate online optimization benchmarks in the design of the loss function for the regression problem, thereby diverging from the use of off-the-shelf regression tools with standard bounds on statistical error.