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.

The classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take them into account. In particular, we study the following online selection problems: (i) the classical secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classical online algorithm for each problem) when the predictions are sufficiently accurate. For each algorithm, we establish a trade-off between the competitive ratios obtained in the two respective cases.

Additional Feedback: Other comments: The MSSR problem mandates that the skier first chooses a shop and then must rent / buy at that same shop for the entire instance. Without this restriction the problem boils down to the standard ski rental problem with rent cost r_i and buy cost b_n since the algorithm can always rent from shop 1 and buy from shop n. It will be good to emphasize the importance of this restriction more in the model. In Lemma 1, the best deterministic online algorithm can choose any of the n shops depending on the argmin of specified term. However, both the randomized and deterministic algorithms that utilize the predictions only buy from either the first shop or the last shop.

This paper builds on prior work for the ski rental problem using predictions. There is interest in this model of online algorithm analysis in the NuerIPS community. However, the paper does not give a lot of new technical insights. I believe this is a borderline paper. It offers a marginal improvement on an area of interest.

Summary and Contributions: Recently there has been a spate of work in online algorithms combining traditional online algorithms with "machine learned" advice. In such problems, one has access to an exogenous prediction about the problem, and one hopes for best of both worlds guarantees of the form: "if the prediction is good, then I do really well (beating the worst-case benchmark), but if the prediction is bad, then I still do (approximately) at least as well as the worst-case benchmark". In the secretary problem, you observe a stream of n real numbers that arrives in a uniformly random order. Your goal is to choose the largest element (or at least achieve a good approximation to the largest element). In the setting with advice, you are given a prediction p of the maximum value of all n real numbers.

The reviewers urge the authors to improve the discussion on how to set c and \lambda, particularly given their relationship with each other.

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 classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take them into account. In particular, we study the following online selection problems: (i) the classical secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classical online algorithm for each problem) when the predictions are sufficiently accurate.

The online assignment problem plays an important role in operational research and computer science which is why immense attention has been given to improving its solution quality. Due to the incomplete information about the input, it is difficult for online algorithms to produce the optimal solution. The quality of the solution of an online algorithm is measured using a competitive ratio. No online deterministic algorithm can achieve a competitive ratio better than (2n-1). It has been shown that advice in online computation improves the lower bound of the competitive ratio of online problems. Advice in online computation can be interpreted as additional information for the online algorithm to compensate for the lack of information about the whole input sequence. In this study, we investigate how introducing machine-learned advice could improve the competitive ratio for this problem. We provide an online algorithm for the online assignment problem by simulating a machine learning algorithm that predicts the whole input in advance. We utilize an optimal offline algorithm to provide a matching solution from the predicted input. Furthermore, we investigate how the prediction error of machine learning affects the competitive ratio of the online algorithm. We utilize a benchmark data set to perform our empirical analysis. We show that as the Machine Learning prediction error increases, the solution quality decreases. Moreover, the magnitude of error is directly proportional to the size of the input. This result is analogous to the competitive ratio of the best deterministic algorithm for the online assignment problem which is dependent also on the parameter n.