Sequential Ski Rental Problem

TL;DR

This paper introduces the sequential ski-rental problem, an online decision-making scenario with unknown costs and season lengths, leveraging expert advice and stochastic assumptions to develop algorithms with proven regret bounds.

Contribution

It extends the classical ski-rental problem by incorporating sequential decision-making with expert advice on costs and durations, under stochastic assumptions.

Findings

Developed online algorithms with regret bounds under stochastic expert advice.

Proved theoretical guarantees for the proposed algorithms.

Experimental results validate the theoretical performance.

Abstract

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.