Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions
Joseph Halpern, Samantha Leung
We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making-minimizing expected regret-to obtain minimax weighted expected regret (MWER).We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.
PDF Link: /papers/12/p336-halpern.pdf
AUTHOR = "Joseph Halpern
and Samantha Leung",
TITLE = "Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions",
BOOKTITLE = "Proceedings of the Twenty-Eighth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-12)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2012",
PAGES = "336--345"