Whittle-indexability of the Cow Path Problem

In this paper we consider the well-studied Cow Path Problem (CPP), an on-line search problem that is typically treated with competitive analysis. This paper uses an alternative approach, posing the problem as a Markov Decision Problem (MDP). Our technical contribution is to prove that when posed as an MDP, a slightly relaxed version of the problem is Whittle-indexable, and we present the corresponding index heuristic. This result also provides an insight: theoretical properties that have been empirically vetted (such as the Whittle index) are a means to bridge the gap between theory and practice in on-line decision-making problems.