Data-Driven Online Decision Making with Costly Information Acquisition

Abstract: In most real-world settings such as recommender systems, finance, and healthcare, collecting useful information is costly and requires an active choice on the part of the decision maker. The decision-maker needs to learn simultaneously what observations to make and what actions to take. This paper incorporates the information acquisition decision into an online learning framework. We propose two different algorithms for this dual learning problem: Sim-OOS and Seq-OOS where observations are made simultaneously and sequentially, respectively. We prove that both algorithms achieve a regret that is sublinear in time. The developed framework and algorithms can be used in many applications including medical informatics, recommender systems and actionable intelligence in transportation, finance, cyber-security etc., in which collecting information prior to making decisions is costly. We validate our algorithms in a breast cancer example setting in which we show substantial performance gains for our proposed algorithms.