We study the problem of augmenting online algorithms with machine learned (ML) advice. In particular, we consider the \emph{multi-shop ski rental} (MSSR) problem, which is a generalization of the classical ski rental problem. In MSSR, each shop has different prices for buying and renting a pair of skis, and a skier has to make decisions on when and where to buy. We obtain both deterministic and randomized online algorithms with provably improved performance when either a single or multiple ML predictions are used to make decisions. These online algorithms have no knowledge about the quality or the prediction error type of the ML prediction. The performance of these online algorithms are robust to the poor performance of the predictors, but improve with better predictions. Extensive experiments using both synthetic and real world data traces verify our theoretical observations and show better performance against algorithms that purely rely on online decision making.
In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known fo…
We consider a variant of the classic Ski Rental online algorithm with applications to machine learning. In our variant, we allow the skier access to a black-box machine-learning algorithm that provides an estimate of the probability that there will be at most a threshold number of ski-days. We derive a class of optimal randomized algorithms to determine the strategy that minimizes the worst-case expected competitive ratio for the skier given a prediction from the machine learning algorithm,and analyze the performance and robustness of these algorithms.
University of Twente（特文特大学）；Tel Aviv University（特拉维夫大学）；Università Bocconi（博科尼大学）；EPFL（洛桑联邦理工学院）；CNRS（法国国家科学研究中心）
We study the online problem of minimizing power consumption in systems with multiple power-saving states. During idle periods of unknown lengths, an algorithm has to choose between power-saving states of different energy consumption and wake-up costs. We develop a learning-augmented online algorithm that makes decisions based on (potentially inaccurate) predicted lengths of the idle periods. The algorithm's performance is near-optimal when predictions are accurate and degrades gracefully with increasing prediction error, with a worst-case guarantee almost identical to the optimal classical onl…
In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a one-time setup cost (``buying price''), and cost proportional to the duration of the usage (``rental rate''). The larger the price, the smaller the rent. The actual usage time is determined by an adversary, and the goal of an algorithm is to minimize the cost by choosing the best option at any point in time. Multislope Ski Rental is a natural generalization of the classical Ski Rental problem…
Algorithms with Calibrated Machine Learning Predictions
Department of Management Science \& Engineering, Stanford University, Stanford, CA, USA；Department of Computer Science, Stanford University, Stanford, CA, USA
University Paris-Saclay（巴黎萨克雷大学）；Sorbonne University（巴黎索邦大学）；IBISC（IBISC（需注意：IBISC是巴黎萨克雷大学下属研究机构，此处按原文提取））；CNRS（法国国家科学研究中心）；LIP6（LIP6（巴黎索邦大学下属实验室，此处按原文提取））
The domain of online algorithms with predictions has been extensively studied for different applications such as scheduling, caching (paging), clustering, ski rental, etc. Recently, Bamas et al., aiming for an unified method, have provided a primal-dual framework for linear covering problems. They extended the online primal-dual method by incorporating predictions in order to achieve a performance beyond the worst-case case analysis. In this paper, we consider this research line and present a framework to design algorithms with predictions for non-linear packing problems. We illustrate the app…
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 regressio…
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 …
Decision-Theoretic Approaches for Improved Learning-Augmented Algorithms
CNRS and International Laboratory on Learning Systems, Montreal, Canada（法国国家科学研究中心及学习系统国际实验室，加拿大蒙特利尔）；Sorbonne University, CNRS, LIP6, Paris, France（索邦大学，法国国家科学研究中心，LIP6，法国巴黎）
A burgeoning paradigm in algorithm design is the field of algorithms with predictions, in which algorithms can take advantage of a possibly-imperfect prediction of some aspect of the problem. While much work has focused on using predictions to improve competitive ratios, running times, or other performance measures, less effort has been devoted to the question of how to obtain the predictions themselves, especially in the critical online setting. We introduce a general design approach for algorithms that learn predictors: (1) identify a functional dependence of the performance measure on the p…
Prediction-Specific Design of Learning-Augmented Algorithms
School of Data Science, The Chinese University of Hong Kong, Shenzhen（数据科学学院，香港中文大学（深圳））；Department of Management Science and Engineering, Stanford University（管理科学与工程系，斯坦福大学）
Online Algorithms via Minimax and Posterior Matching
University of Bonn（波恩大学）；Institute of Computer Science, University of Bonn（波恩大学计算机科学学院）；Microsoft Research（微软研究院）；PUC-Rio（里约热内卢天主教大学）；Georgia Tech（佐治亚理工学院）；School of Mathematics, Georgia Tech（佐治亚理工学院数学学院）；School of Computer Science, Georgia Tech（佐治亚理工学院计算机科学学院）
In this paper, we explicitly study the online vertex cover problem, which is a natural generalization of the well-studied ski-rental problem. In the online vertex cover problem, we are required to maintain a monotone vertex cover in a graph whose vertices arrive online. When a vertex arrives, all its incident edges to previously arrived vertices are revealed to the algorithm. For bipartite graphs with the left vertices offline (i.e. all of the left vertices arrive first before any right vertex), there are algorithms achieving the optimal competitive ratio of $\frac{1}{1-1/e}\approx 1.582$. Our…
