Ola Hössjer: A mathematical framework for learning and knowledge acquisition

Abstract

Knowledge about propositions or facts is usually referred to as justified, true belief. I will use this as a starting point for providing a mathematical framework for how an agent learns and acquires knowledge, with four main ingredients: 1) A set of possible parameter values or worlds which the agent has to choose between, 2) A Bayesian approach for quantifying belief as a posterior distribution on the set of possible worlds, 3) A frequentist approach, by which one world as true whereas the others are counterfactuals, 4) A sigma algebra that sets the limit to the extent at which data can be used to discriminate between the possible worlds. Based on these four ingredients, learning is defined as true belief, whereas knowledge acquisition additionally requires that this belief is formed for the right reason, in terms of belief in the true world. Examples are given from scoring of online math tests and game theory. We will finally argue that chat robots may learn, but never acquires knowledge, about moral values. The talk is based on joint work with Daniel Diaz and Sunil Rao.