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.

We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when predictions are accurate and maintains worst-case guarantees. Such algorithms have been studied in a recent line of works due to Lykouris and Vassilvitskii (ICML '18) and Purohit et al (NeurIPS '18). They provide robustness-consistency trade-offs for a variety of online problems. However, they leave open the question of whether these trade-offs are tight, i.e., to what extent to such trade-offs are necessary. In this paper, we provide the first set of non-trivial lower bounds for competitive analysis using machine-learned predictions. We focus on the classic problems of ski-rental and non-clairvoyant scheduling and provide optimal trade-offs in various settings.

Summary and Contributions: The paper considers the problem of designing online algorithms that utilize machine learning predictions for the ski rental and non-clairvoyant scheduling problem. In the learning augmented setup, the consistency of an algorithm is defined to be its competitive ratio given perfect predictions whereas the robustness of an algorithm is defined to be its competitive ratio when the predictions are arbitrarily erroneous. Unlike most recent work in this area, the paper focuses on providing lower bounds on the tradeoffs between robustness and consistency in this framework. In particular, they show that for the ski rental problem the learning augmented algorithms of [42] actually yield the optimum tradeoff between robustness and consistency (for both deterministic and randomized algorithms). The proofs of these lower bounds are non-trivial but not surprising.

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.

We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when predictions are accurate and maintains worst-case guarantees. Such algorithms have been studied in a recent line of works due to Lykouris and Vassilvitskii (ICML '18) and Purohit et al (NeurIPS '18). They provide robustness-consistency trade-offs for a variety of online problems. However, they leave open the question of whether these trade-offs are tight, i.e., to what extent to such trade-offs are necessary.

Learning-augmented algorithms has been extensively studied recently in the computer-science community, due to the potential of using machine learning predictions in order to improve the performance of algorithms. Predictions are especially useful for online algorithms making irrevocable decisions without knowledge of the future. Such learning-augmented algorithms aim to overcome the limitations of classical online algorithms when the predictions are accurate, and still perform comparably when the predictions are inaccurate. A common approach is to adapt existing online algorithms to the particular advice notion employed, which often involves understanding previous sophisticated algorithms and their analyses. However, ideally, one would simply use previous online solutions in a black-box fashion, without much loss in the approximation guarantees. Such clean solutions that avoid opening up black-boxes are often rare, and may be even missed the first time around. For example, Grigorescu et al. (NeurIPS 22) proposed a learning-augmented algorithms for online covering linear programs, but it later turned out that their results can be subsumed by a natural approach that switches between the advice and an online algorithm given as a black-box, as noted in their paper. In this work, we introduce and analyze a simple learning-augmented algorithm for online packing problems with linear constraints and concave objectives. We exhibit several direct applications of our framework including online packing linear programming, knapsack, resource management benefit, throughput maximization, and network utility maximization. We further raise the problem of understanding necessary and sufficient conditions for when such simple black-box solutions may be optimal. We believe this is an important direction of research that would unify many ad-hoc approaches from the literature.