Exploration-exploitation of functions, that is learningand optimizing a mapping between inputs and expectedoutputs, is ubiquitous to many real world situations.These situations sometimes require us to avoid certainoutcomes at all cost, for example because they arepoisonous, harmful, or otherwise dangerous. We testparticipants’ behavior in scenarios in which they haveto find the optimum of a function while at the sametime avoid outputs below a certain threshold. Intwo experiments, we find that Safe-Optimization, aGaussian Process-based exploration-exploitation algo-rithm, describes participants’ behavior well and thatparticipants seem to care first about whether a point issafe and then try to pick the optimal point from all suchsafe points. This means that their trade-off betweenexploration and exploitation indicates intelligent,approximate, and homeostasis-driven behavior