Ronen I. Brafman
Moshe Tennenholtz
Skip Abstract Section
Abstract
The need for computationally efficient decision-making techniques together with the desire to simplify the processes of knowledge acquisition and agent specification have led various researchers in artificial intelligence to examine qualitative decision tools. However, the adequacy of such tools is not clear. This paper investigates the foundations of maximin, minmax regret, and competitive ratio, three central qualitative decision criteria, by characterizing those behaviors that could result from their use. This characterizaton provides two important insights: (1)under what conditions can we employ an agent model based on these basic qualitative decision criteria, and (2) how “rational” are these decision procedures. For the competitive ratio criterion in particular, this latter issue is of central importance to our understanding of current work on on-line algorithms. Our main result is a constructive representation theorem that uses two choice axioms to characterize maximin, minmax regret, and competitive ratio.
- ALLEN, J., HENDLER, J., AND TATE, A., EDS. 1990. Readings in Planning. Morgan-Kaufmann, San Francisco, Calif.Google Scholar
- ANSCOMBE, F. J., AND AUMANN, R.J. 1963. A definition of subjective probability. Ann. Math. Stat. 34, 199-205.Google Scholar
- BLUM, L., BRANDENBURGER, A., AND DEKEL, E. 1991. Lexicographic probabilities and equilibrium refinements. Econometrica 59, 61-79.Google Scholar
- BORODIN, A., AND EL-YANIV, R. 1998. On-Line Computation and Competitive Analysis. Cambridge University Press, Cambridge, Mass. Google Scholar
- BOUTILIER, C. 1994. Toward a Logic for Qualitative Decision Theory. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning. Morgan-Kaufmann, San Francisco, Calif., pp. 75-86.Google Scholar
- BOUTILIER, C., BRAFMAN, R. I., GEIB, C., AND POOLE, D. 1997. Reasoning with ceteris paribus preference statements. In Proceedings of the AAAI Spring Symposium on Qualitative Preferences in Deliberation and Practical Reasoning. AAAI Press, Menlo Park, Calif.Google Scholar
- BRAFMAN, R. I., AND FRIEDMAN, N. 1995. On decision-theoretic foundations for defaults. In Proceedings of the 14th International Joint Conference on Artificial Intelligence. Google Scholar
- BRAFMAN, R. I., AND TENNENHOLTZ, M. 1994. Belief ascription and mental-level modelling. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning, J. Doyle, E. Sandewall, and P. Torasso, Eds., pp. 87-98.Google Scholar
- BRAFMAN, R., AND TENNENHOLTZ, M. 1997. Modeling agents as qualitative decision-makers. Artif. Int. 94, 217-268. Google Scholar
- COOPER, G. F. 1990. The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Int. 42, 2-3, 393-405. Google Scholar
- DARWICHE, A., AND GOLDSZMIDT, M. 1994. On the relation between kappa calculus and probabilistic reasoning. In Proceedings of the lOth Conference on Uncertainty in Artificial Intelligence (UAI '94). Morgan-Kaufmann, San Francisco, Calif., pp. 145-153.Google Scholar
- DOYLE, J. 1989. Constructive belief and rational representation. Comput. Int. 5, 1-11. Google Scholar
- DOYLE, J., AND THOMASON, R. 1997. Qualitative preferences in deliberation and practical reasoning. Working notes of the AAAI spring symposium.Google Scholar
- DOYLE, J., AND WELLMAN, M. 1994. Representing preferences as ceteris paribus comparatives. In Proceedings of the AAAI Spring Symposium on Decision-Theoretic Planning. AAAI Press, Menlo Park, Calif., pp. 69-75.Google Scholar
- DOYLE, J., AND WELLMAN, M.P. 1989. Impediments to universal preference-based default theories. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, (Toronto, Ont., Canada, May). Ron Brachman and Hector Levesque, Eds. Morgan- Kaufmann, San Francisco, Calif., pp. 94-102. Google Scholar
- DUBOIS, D., AND PRADE, H. 1995. Possibility theory as a basis for qualitative decision theory. In Proceedings of the 14th International Joint Conference on Artificial Intelligence. pp. 1924-1930.Google Scholar
- DUBOIS, D., PRADE, H., AND SABBADIN, R. 2000. Decision-theoretic foundations of qualitative possibility theory. Europ. J. Oper. Res., to appear.Google Scholar
- EL-YANIV, R. 2000. On the decision theoretic foundations of the competative ratio criterion. Unpublished manuscript.Google Scholar
- FAGIN, R., HALPERN, J. Y., MOSES, Y., AND VARDI, M.Y. 1995. Reasoning about Knowledge. MIT Press, Cambridge, Mass. Google Scholar
- FISHBURN, P. C. 1988. Nonlinear Preference and Utility Theory. Johns Hopkins University Press, Baltimore, Md.Google Scholar
- FORBUS, K.D. 1985. Qualitative process theory. In Qualitative Reasoning About Physical Systems. D. Bobrow, Ed. The MIT Press, Cambridge, Mass.Google Scholar
- FRIEDMAN, N., AND HALPERN, J.Y. 1994. A knowledge-based framework for belief change. Part I: Foundations. In Proceedings of the 5th Conference on Theoretical Aspects of Reasoning About Knowledge, Morgan-Kaufmann, San Francisco, Calif. pp. 44-64. Google Scholar
- FUDENBERG, D., AND TIROLE, J. 1991. Game Theory. MIT Press, Cambridge, Mass.Google Scholar
- GARDENFORS, P. 1992. Belief Revision. Cambridge University Press, Cambridge, Mass. Google Scholar
- GILBOA, I., AND SCHMEIDLER, D. 1989. Maxmin expected utility with a non-unique prior. J. Math. Econ. 18, 141-153.Google Scholar
- GILBOA, I., AND SCHMEIDLER, D. 1995. Case-based decision theory. Quart. J. Econ. 110, 605-639.Google Scholar
- GINSBERG, M. L., ED. 1987. Readings in Nonmonotonic Reasoning. Morgan-Kaufmann, San Francisco, Calif. Google Scholar
- HALPERN, J.Y. 1988. Reasoning about knowledge: An overview. In Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1988 Conference. Morgan-Kaufmann, San Francisco, Calif., pp. 1-17. Google Scholar
- HALPERN, J. Y., AND MOSES, Y. 1990. Knowledge and common knowledge in a distributed environment. J. ACM 37, (3) (July), 549-587. Google Scholar
- HART, S., MODICA, S., AND SCHMEIDLER, D. 1994. A neo-Bayesian foundation of the maxmin value for two-parson zero-sum games. Int. J. Game Theory, 23:347-358 Google Scholar
- HOWARD, R.A. 1960. Dynamic Programming and Markov Processes. MIT Press, Cambridge, Mass.Google Scholar
- KREPS, D.M. 1988. Notes on the Theory of Choice. Westview Press, Boulder, Colo.Google Scholar
- LAMARRE, P., AND SHOHAM, Y. 1994. Knowledge, certainty, belief and conditionalization. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning. Morgan-Kaufmann, San Francisco, Calif., pp. 415-424.Google Scholar
- LEHMANN, D. 1996. Generalized qualitative probability: Savage revisited. In Proceedings of the 12th Annual Conference on Uncertainty in Artificial Intelligence (UAI '96). Morgan-Kaufmann, San Francisco, Calif., pp. 381-388. Google Scholar
- LEVESQUE, H. 1986. Knowledge representation and reasoning. Ann. Rev. Comput. Sci. 1,255-287. Google Scholar
- LUCE, R. D., AND RAIFFA, H. 1957. Games and Decisions. Wiley, New York.Google Scholar
- MmNOR, J. 1954. Games against nature. In Decision Processes, R. M. Thrall, C. H. Coombs, and R. L. Davis, Eds. Wiley, New York.Google Scholar
- PAPADIMITRIOU, C. H., AND YANNAKAKIS, M. 1989. Shortest paths without a map. In Automata, Languages and Programming. 16th International Colloquium Proceedings. pp. 610-620. Google Scholar
- ROSENSCHEIN, S.J. 1985. Formal theories of knowledge in AI and robotics. New Gen. Comput. 3, 3, 345-357. Google Scholar
- SAVAGE, L.J. 1972. The Foundations of Statistics. Dover Publications, New York.Google Scholar
- SHIMONY, S.E. 1994. Finding MAPs for belief networks is NP-hard. Artif. Int. 68, (2) (Aug.), pp. 399-410. Google Scholar
- TAN, S., AND PEARL, J. 1994. Qualitative decision theory. In Proceedings of the 12th National Conference on Artificial Intelligence. Morgan-Kaufmann, San Francisco, Calif., pp. 928-932. Google Scholar
- TAN, S. W., AND PEARL, J. 1994. Specification and evaluation of preferences under uncertainty. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning. pp. 530-539.Google Scholar
- VON NEUMANN, J., AND MORGENSTERN, 0. 1944. Theory of Games and Economic Behavior. Princeton University Press, Princeton, N. J.Google Scholar
- WALD, A. 1950. Statistical Decision Functions. Wiley, New York.Google Scholar
- ZADEH, L.A. 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy sets syst. 1, 3-28.Google Scholar
Index Terms
- An axiomatic treatment of three qualitative decision criteria
Recommendations
Qualitative decision theory: from savage's axioms to nonmonotonic reasoning
This paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible, in the scope of artificial intelligence. Contrary to classical approaches to decision theory, we try to rank acts without resorting to any ...
Hesitant Fuzzy Linguistic VIKOR Method and Its Application in Qualitative Multiple Criteria Decision Making
The hesitant fuzzy linguistic term set (HFLTS) has turned out to be a powerful and flexible technique in representing decision makers' qualitative assessments in the processes of decision making. The aim of this paper is to develop a method to solve the ...
On the axiomatization of qualitative decision criteria
AAAI'97/IAAI'97: Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligenceQualitative decision tools have been used in AI and CS in various contexts, but their adequacy is still unclear. To examine this question, our work employs the axiomatic approach to characterize the properties of various decision rules. In the past, we ...
Comments