Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions
This work addresses a foundational issue in decision theory and AI for agents dealing with uncertainty, offering a novel representation and decision rule, though it appears incremental as it builds on existing minimax regret frameworks.
The paper tackles the problem of representing uncertainty with sets of probability measures, which can fail to learn appropriately during updating, by proposing weighted sets of probabilities with a method for updating and weighting, and introduces minimax weighted expected regret (MWER) for decision-making, providing axiomatizations for static and dynamic preferences.
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.