Machine learning advised algorithms for the ski rental problem with a discount

Abstract

Traditional online algorithms are designed to make decisions online in the face of uncertainty to perform well compared to the optimal offline algorithm for the worst-case inputs. On the other hand, machine learning algorithms try to extrapolate the pattern from the past inputs to predict the future and take decisions online based on the predictions to perform well for the average-case inputs. Recent studies have augmented traditional online algorithms with machine learning oracles to get better performance for all the possible inputs. The machine learning augmented online algorithms perform provably better than the traditional online algorithms when the error of the machine learning oracle is low for the worst-case inputs and all other average-case inputs. Even when the advice from the machine learning oracle is poor, the machine learning advised algorithms are robust, hence do not degrade abruptly with worst-case inputs.In this article, we integrate the advantages of traditional online algorithms and machine learning algorithms in the context of a novel variant of the ski rental problem. Firstly, we propose the ski rental problem with a discount: in this problem, the rent of the ski, instead of being fixed over time, varies as a function of time. Secondly, we discuss the design and performance evaluation of the online algorithms with machine learning advice to solve the ski rental problem with a discount. Finally, we extend this study to the situation where multiple independent machine learning advice is available. This algorithm design framework motivates redesigning several online algorithms by augmenting them with one or more machine learning oracles to improve their performance.