Abstract
In Part II, we focus on decentralized stochastic control problems and their applications. In Chapter 8, we present our results on the finite model approximation of multi-agent stochastic control problems (team decision problems). We show that optimal strategies obtained from finite models approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, we show that quantized team policies are asymptotically optimal. In Chapter 9, the results are applied to Witsenhausen’s counterexample and the Gaussian relay channel problem.
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References
M. Andersland, D. Teneketzis, Information structures, causality, and non-sequential stochastic control, I: design-independent properties. SIAM J. Control Optim. 30, 1447–1475 (1992)
M. Andersland, D. Teneketzis, Information structures, causality, and non-sequential stochastic control, II: design-dependent properties. SIAM J. Control Optim. 32, 1726–1751 (1994)
C.D. Charalambous, N.U. Ahmed, Equivalence of decentralized stochastic dynamic decision systems via Girsanov’s measure transformation, in IEEE Conference on Decision and Control (CDC) (IEEE, Los Angeles, 2014), pp. 439–444
P.R. De Waal, J.H. Van Schuppen, A class of team problems with discrete action spaces: optimality conditions based on multimodularity. SIAM J. Control Optim. 38(3), 875–892 (2000)
A. Gupta, S. Yüksel, T. Basar, C. Langbort, On the existence of optimal policies for a class of static and sequential dynamic teams. SIAM J. Control Optim. 53(3), 1681–1712 (2015)
Y.C. Ho, K.C. Chu, Team decision theory and information structures in optimal control problems - part I. IEEE Trans. Autom. Control 17, 15–22 (1972)
Y.C. Ho, K.C. Chu, On the equivalence of information structures in static and dynamic teams. IEEE Trans. Autom. Control 18(2), 187–188 (1973)
J.C. Krainak, J.L. Speyer, S.I. Marcus, Static team problems – part I: sufficient conditions and the exponential cost criterion. IEEE Trans. Autom. Control 27, 839–848 (1982)
R. Radner, Team decision problems. Ann. Math. Stat. 33, 857–881 (1962)
D. Teneketzis, On information structures and nonsequential stochastic control. CWI Q. 9, 241–260 (1996)
H.S. Witsenhausen, A counterexample in stochastic optimum control. SIAM J. Control Optim. 6(1), 131–147 (1968)
H.S. Witsenhausen, On information structures, feedback and causality. SIAM J. Control 9, 149–160 (1971)
H.S. Witsenhausen, The intrinsic model for discrete stochastic control: some open problems, in Control Theory, Numerical Methods and Computer Systems Modelling Lecture Notes in Economics and Mathematical Systems, vol. 107 (Springer, Berlin, 1975), pp. 322–335
H.S. Witsenhausen, Equivalent stochstic control problems. Math. Control Signal Syst. 1(1), 3–11 (1988)
Y. Wu, S. Verdú, Witsenhausen’s counterexample: a view from optimal transport theory, in Proceedings of the IEEE Conference on Decision and Control, Florida, USA (2011), pp. 5732–5737
S Yüksel, T. Başar, Stochastic Networked Control Systems: Stabilization and Optimization Under Information Constraints (Springer, New York, 2013)
S. Yüksel, N. Saldi, Convex analysis in decentralized stochastic control, strategic measures and optimal solutions. SIAM J. Control Optim. 55(1), 1–28 (2017)
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Saldi, N., Linder, T., Yüksel, S. (2018). Prelude to Part II. In: Finite Approximations in Discrete-Time Stochastic Control. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-79033-6_7
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DOI: https://doi.org/10.1007/978-3-319-79033-6_7
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