AIJan 31, 2015
Minimizing Regret in Dynamic Decision ProblemsJoseph Y. Halpern, Samantha Leung
The menu-dependent nature of regret-minimization creates subtleties when it is applied to dynamic decision problems. Firstly, it is not clear whether \emph{forgone opportunities} should be included in the \emph{menu}, with respect to which regrets are computed, at different points of the decision problem. If forgone opportunities are included, however, we can characterize when a form of dynamic consistency is guaranteed. Secondly, more subtleties arise when sophistication is used to deal with dynamic inconsistency. In the full version of this paper, we examine, axiomatically and by common examples, the implications of different menu definitions for sophisticated, regret-minimizing agents.
AIJan 21, 2015
Maximin Safety: When Failing to Lose is Preferable to Trying to WinBrad Gulko, Samantha Leung
We present a new decision rule, \emph{maximin safety}, that seeks to maintain a large margin from the worst outcome, in much the same way minimax regret seeks to minimize distance from the best. We argue that maximin safety is valuable both descriptively and normatively. Descriptively, maximin safety explains the well-known \emph{decoy effect}, in which the introduction of a dominated option changes preferences among the other options. Normatively, we provide an axiomatization that characterizes preferences induced by maximin safety, and show that maximin safety shares much of the same behavioral basis with minimax regret.
GTFeb 21, 2013
Weighted Sets of Probabilities and Minimax Weighted Expected Regret: New Approaches for Representing Uncertainty and Making DecisionsJoseph Y. 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-by-measure 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.
GTOct 16, 2012
Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making DecisionsJoseph Y. 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.