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 less than 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.

We consider a generalization of the classical Ski Rental Problem motivated by applications in cloud computing. We develop deterministic and probabilistic online algorithms for rent/buy decision problems with time-varying demand. We show that these algorithms have competitive ratios of 2 and 1.582 respectively. We also further establish the optimality of these algorithms. 233

Healthcare providers are increasingly using machine learning to predict patient outcomes to make meaningful interventions. However, despite innovations in this area, deep learning models often struggle to match performance of shallow linear models in predicting these outcomes, making it difficult to leverage such techniques in practice. In this work, motivated by the task of clinical prediction from insurance claims, we present a new technique called reverse distillation which pretrains deep models by using high-performing linear models for initialization. We make use of the longitudinal structure of insurance claims datasets to develop Self Attention with Reverse Distillation, or SARD, an architecture that utilizes a combination of contextual embedding, temporal embedding and self-attention mechanisms and most critically is trained via reverse distillation. SARD outperforms state-of-the-art methods on multiple clinical prediction outcomes, with ablation studies revealing that reverse distillation is a primary driver of these improvements. Code is available at https://github.com/clinicalml/omop-learn.

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