Witsenhausen's counterexample: A view from optimal transport theory

Yihong Wu; Sergio Verdú

doi:10.1109/CDC.2011.6160829

Witsenhausen's counterexample: A view from optimal transport theory

Yihong Wu, Sergio Verdú

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We formulate Witsenhausen's decentralized stochastic control setup as an optimization problem involving the quadratic Wasserstein distance and the minimum mean-square error. Classical results are recovered as immediate consequences of transport-theoretic properties. New results and bounds on the optimal cost are also obtained. In particular, we show that the optimal controller is a strictly increasing function with a real analytic left inverse.

Original language	English (US)
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages	5732-5737
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2011.6160829
State	Published - Dec 1 2011
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: Dec 12 2011 → Dec 15 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country	United States
City	Orlando, FL
Period	12/12/11 → 12/15/11

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2011.6160829

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Witsenhausen's counterexample : A view from optimal transport theory. / Wu, Yihong; Verdú, Sergio.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 5732-5737 6160829 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Wu, Y & Verdú, S 2011, Witsenhausen's counterexample: A view from optimal transport theory. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160829, Proceedings of the IEEE Conference on Decision and Control, pp. 5732-5737, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160829

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