A Regression Approach to Learning-Augmented Online Algorithms

Keerti Anand, Rong Ge, Amit Kumar, Debmalya Panigrahi

Keywords: Learning Aided Algorithm Design, learning augmented online algorithms, learning theory, Optimization, Algorithms under uncertainty

TL;DR: This paper gives a regression-based framework for learning-augmented online algorithms that applies to a broad variety of problems such as (generalized) ski rental, online bin packing, online scheduling, etc.

Abstract: 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.

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