Stochastic teams with nonclassical information revisited: When is an affine law optimal?
- 1 June 1987
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 32 (6) , 554-559
- https://doi.org/10.1109/tac.1987.1104636
Abstract
In this note we consider a parameterized family of two-stage stochastic control problems with nonclassical information patterns, which includes the well-known 1968 counterexample of Witsenhausen. We show that whenever the performance index does not contain a product term between the decision variables, the optimal solution is linear in the observation variables. The parameter space can be partitioned into two regions in one of which the optimal solution is linear, whereas in the other it is inherently nonlinear. Extensive computations using two-point piecewise constant policies and linear plus piecewise constant policies provide numerical evidence that nonlinear policies may indeed outperform linear policies when the product term is present.Keywords
This publication has 9 references indexed in Scilit:
- Intractable problems in control theoryPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1985
- On the complexity of decentralized decision making and detection problemsIEEE Transactions on Automatic Control, 1985
- Team decision theory and information structuresProceedings of the IEEE, 1980
- Simultaneous communication and controlAdvances in Applied Probability, 1976
- The Intrinsic Model for Discrete Stochastic Control: Some Open ProblemsPublished by Springer Nature ,1975
- Information structure in dynamic multi-person control problemsAutomatica, 1974
- Team decision theory and information structures in optimal control problems--Part IIEEE Transactions on Automatic Control, 1972
- Another look at the coding theorem of information theory—A tutorialProceedings of the IEEE, 1970
- A Counterexample in Stochastic Optimum ControlSIAM Journal on Control, 1968