Inspired by the human ability to perform complex manipulation in the complete absence of vision (like retrieving an object from a pocket), the robotic manipulation field is motivated to develop new methods for tactile-based object interaction. However, tactile sensing presents the challenge of being an active sensing modality: a touch sensor provides sparse, local data, and must be used in conjunction with effective exploration strategies in order to collect information. In this work, we focus on the process of guiding tactile exploration, and its interplay with task-related decision making. We propose TANDEM (TActile exploration aNd DEcision Making), an architecture to learn efficient exploration strategies in conjunction with decision making. Our approach is based on separate but co-trained modules for exploration and discrimination. We demonstrate this method on a tactile object recognition task, where a robot equipped with a touch sensor must explore and identify an object from a known set based on tactile feedback alone. TANDEM achieves higher accuracy with fewer actions than alternative methods and is also shown to be more robust to sensor noise.