Sequential Ski Rental Problem

The classical 'buy or rent' ski-rental problem was recently considered in the setting where multiple experts (such as Machine Learning algorithms) advice on the length of the ski season. Here, robust algorithms were developed with improved theoretical performance over adversarial scenarios where such expert predictions were unavailable. We consider a variant of this problem which we call the 'sequential ski-rental' problem. Here, a sequence of ski-rental problems has to be solved in an online fashion where both the buy cost and the length of the ski season are unknown to the learner. The learner has access to two sets of experts, one set who advise on the true cost of buying the ski and another set who advise on the length of the ski season. Under certain stochastic assumptions on the experts who predict the buy costs, we develop online algorithms and prove regret bounds for the same. Our experimental evaluations confirm our theoretical results.