Abstract
Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aoki, M.: 1977, ‘Adaptive Control Theory: Survey and Potential Applications to Decision Processes’, Invited Paper, presented at the Stochastic Control Workship, AIDS National Meeting, Chicago.
Arrow, K.: 1965,Aspects of the Theory of Risk Bearing, Yrjo Johnsson Foundation, Helsinki.
Barnett, V.: 1973,Comparative Statistical Inference, New York, John Wiley & Sons.
Bellman, R. and Kalaba, R.: 1957, ‘On the Role of Dynamic Programming in Statistical Communication Theory’, IRETransactions on Information Theory, IT-3, 197–203.
De Finetti, B.: 1970,Theory of Probability, Vol. 1, New York: John Wiley & Sons.
DeGroot, M.: 1970,Optimal Statistical Decisions, New York, McGraw-Hill.
Fienberg, S. and Zellner, A. eds.: 1975,Studies in Bayesian Econometrics and Statistics, Amsterdam, North-Holland Publishing Company.
Harrison, P. and Stevens, C.: 1976, ‘Bayesian Forecasting’,Journal of the Royal Statistical Society, Series B,38, 205–247.
Hinderer, K.: 1970,Foundations of Non-Stationary Dynamic Programming with Discrete Time Parameter, New York, Springer Verlag.
Kalaba, R. and Tesfatsion, L.: 1978, ‘Two Solution Techniques for Adaptive Reinvestment: A Small Sample Comparison’,Journal of Cybernetics 8, 101–111.
Kalman, R.: 1978, ‘A Retrospective After Twenty Years: From the Pure to the Applied’, Invited Paper, Chapman Conference on Applications of the Kalman Filter, Pittsburgh, forthcoming inApplied Mathematics and Computation.
Lindley, D.: 1971,Bayesian Statistics: A Review, Philadelphia: SIAM.
Saridis, G.: 1977,Self-Organizing Control of Stochastic Systems, New York, Marcel Dekker.
Tesfatsion, L.: 1976, ‘Bayes' Theorem for Utility’, Discussion Paper 76-65, Center for Economic Research, University of Minnesota.
Testfatsion, L.: 1978, ‘A New Approach to Filtering and Adaptive Control’,Journal of Optimization Theory and Applications 25, 247–261.
Tesfatsion, L.: 1978, ‘A New Approach to Filtering and Adaptive Control: Stability Results’,Applied Mathematics and Computation 4, 27–44.
Tesfatsion, L.: 1977, ‘A New Approach to Filtering and Adaptive Control: Optimality Results’,Journal of Cybernetics 7, 133–146.
Tesfatsion, L.: 1979, ‘Direct Updating of Intertemporal Criterion Functions for a Class of Adaptive Control Problems’, IEEETransactions on Systems, Man, and Cybernetics, SMC-9, 143–151.
Tesfatsion, L.: 1979, ‘Criterion Filtering Methods for Adaptive Control’,Proceedings, 12th Annual Asilomar Conference on Circuits, Systems, and Computers, Pacific Grove, California, IEEE Computer Society, 73–76.
Tesfatsion, L.: 1980a, ‘A Conditional Expected Utility Model for Myopic Decision Makers’,Theory and Decision,12, 185–206.
Tesfatsion, L.: 1980b, ‘Global and Approximate Global Optimality of Myopic Economic Decisions’,Journal of Economic Dynamics and Control 2, 135–160.
Tesfatsion, L.: 1980c, ‘C 3 Modeling with Symmetrical Rationality’,Applied Mathematics and Computation,6, 51–61.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tesfatsion, L. A dual approach to Bayesian inference and adaptive control. Theor Decis 14, 177–194 (1982). https://doi.org/10.1007/BF00133976
Issue Date:
DOI: https://doi.org/10.1007/BF00133976