Gesture recognition systems often require high-resolution images of hands and faces, but the issue of how to choose which body features to observe is often left unresolved or only addressed with hard-coded solutions. In this paper we have presented a mechanism to learn to selectively foveate salient body parts in an active gesture recognition task. We adopt a Partially Observable Markov Decision Process formalism, using an action set comprised of foveation actions as well as a special recognition action. Execution of this action is rewarded based on whether the target is in the scene. We use instance-based hidden state reinforcement learning to learn a policy which models both when to execute the recognition action and what foveation commands to execute to properly discriminate the target gesture. To accurately pool experience when estimating the utility of a new action, we implement a variable-K nearest neighbor algorithm which includes all experience with a given action chain. These methods learn successful recognition policies but can consume large amounts of memory, which leads to inefficient run-time performance. To overcome this we demonstrated how to transform the learned action-selection policy representation into a concise visual behavior based on an augmented Finite State Machine representation.