Learning Agents with Evolving Hypothesis Classes

It has recently been shown that a Bayesian agent with a universal hypothesis class resolves most induction problems discussed in the philosophy of science. These ideal agents are, however, neither practical nor a good model for how real science works. We here introduce a framework for learning based on implicit beliefs over all possible hypotheses and limited sets of explicit theories sampled from an implicit distribution represented only by the process by which it generates new hypotheses. We address the questions of how to act based on a limited set of theories as well as what an ideal sampling process should be like. Finally, we discuss topics in philosophy of science and cognitive science from the perspective of this framework.