Research note: A representation theorem for minmax regret policies

Authors:
Sanjiang Li
Affiliations:
State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China and Institut für Informatik, Albert-Ludwi ...
Venue:
Artificial Intelligence
Year:
2007

Citing 4
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Shortest paths without a map

Theoretical Computer Science
Qualitative decision theory

AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
An axiomatic treatment of three qualitative decision criteria

Journal of the ACM (JACM)
Qualitative decision theory with preference relations and comparative uncertainty: an axiomatic approach

Artificial Intelligence - Special issue: Fuzzy set and possibility theory-based methods in artificial intelligence

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Abstract

Decision making under uncertainty is one of the central tasks of artificial agents. Due to their simplicity and ease of specification, qualitative decision tools are popular in artificial intelligence. Brafman and Tennenholtz [R.I. Brafman, M. Tennenholtz, An axiomatic treatment of three qualitative decision criteria, J. ACM 47 (3) (2000) 452-482] model an agent's uncertain knowledge as her local state, which consists of states of the world that she deems possible. A policy determines for each local state a total preorder of the set of actions, which represents the agent's preference over these actions. It is known that a policy is maximin representable if and only if it is closed under unions and satisfies a certain acyclicity condition. In this paper we show that the above conditions, although necessary, are insufficient for minmax regret and competitive ratio policies. A complete characterization of these policies is obtained by introducing the best-equally strictness.