Learning to control a safety-critical system with latent dynamics (e.g. for deep brain stimulation) requires taking calculated risks to gain information as efficiently as possible. To address this problem, we present a probabilistically-safe, meta-active learning approach to efficiently learn system dynamics and optimal configurations. We cast this problem as meta-learning an acquisition function, which is represented by a Long-Short Term Memory Network (LSTM) encoding sampling history. This acquisition function is meta-learned offline to learn high quality sampling strategies. We employ a mixed-integer linear program as our policy with the final, linearized layers of our LSTM acquisition function directly encoded into the objective to trade off expected information gain (e.g., improvement in the accuracy of the model of system dynamics) with the likelihood of safe control. We set a new state-of-the-art in active learning for control of a high-dimensional system with altered dynamics (i.e., a damaged aircraft), achieving a 46% increase in information gain and a 20% speedup in computation time over baselines. Furthermore, we demonstrate our system's ability to learn the optimal parameter settings for deep brain stimulation in a rat's brain while avoiding unwanted side effects (i.e., triggering seizures), outperforming prior state-of-the-art approaches with a 58% increase in information gain. Additionally, our algorithm achieves a 97% likelihood of terminating in a safe state while losing only 15% of information gain.