Active function learning as Gaussian Process optimization

How can and should an agent actively learn a function? Psychological theories about function learning are vast, but currently there is no real theory about how humans actively acquire knowledge about continuous input-output relations. We try to develop atheory of active function learning based on Gaussian Processes, a non-parametric class of regression models that can learn functions in a close to-rational manner.It will be shown how Gaussian processes can be used to explore and exploit stationary functions based on greedy algorithms and mathematical properties of these algorithms will be stated. Moving on, two generalized algorithms that allow many classes of models to be utilized within exploration/exploitation scenarios will be introduced.All of the stated models will then be tested at how well they can explore or exploit a 2- dimensional function in an a priori simulation study. Afterwards, 2 different experimentswill be introduced in which human participants had to explore or exploit the different 2d-functtions. It will be shown that Gaussian Processes can indeed provide a powerful tool to model human active function learning, beating all of the alternativemodels in every single experiment.