Optimal Sequential Exploration: A Binary Learning Model

In this paper, we develop a practical and flexible framework for evaluating sequential exploration strategies in the case where the exploration prospects are dependent. Our interest in this problem was motivated by an oil exploration problem, and our approach begins with marginal assessments for each prospect (e.g., what is the probability that the well is wet?) and pairwise assessments of the dependence between prospects (e.g., what is the probability that both wells i and j are wet?). We then use information-theoretic methods to construct a full joint distribution for all outcomes from these marginal and pairwise assessments. This joint distribution is straightforward to calculate, has many nice properties, and appears to provide an accurate approximation for distributions likely to be encountered in practice. Given this joint probability distribution, we determine an optimal drilling strategy using an efficient dynamic programming model. We illustrate these techniques with an oil exploration example and study how dependence and risk aversion affect the optimal drilling strategies. The information-theory-based techniques for constructing joint distributions and dynamic programming model for determining optimal exploration strategies could be used together or separately in many other applications.