Learning approaches to the Witsenhausen counterexample from a view of potential games

Na Li; Jason R. Marden; Jeff S. Shamma

doi:10.1109/CDC.2009.5400596

Learning approaches to the Witsenhausen counterexample from a view of potential games

Na Li^*, Jason R. Marden, Jeff S. Shamma

^*Corresponding author for this work

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

22 Scopus citations

Abstract

Since Witsenhausen put forward his remarkable counterexample in 1968, there have been many attempts to develop efficient methods for solving this non-convex functional optimization problem. However there are few methods designed from game theoretic perspectives. In this paper, after discretizing the Witsenhausen counterexample and re-writing the formulation in analytical expressions, we use fading memory JSFP with inertia, one learning approach in games, to search for better controllers from a view of potential games. We achieve a better solution than the previously known best one. Moreover, we show that the learning approaches are simple and automated and they are easy to extend for solving general functional optimization problems.

Original language	English (US)
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	157-162
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5400596
State	Published - 2009
Externally published	Yes
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: Dec 15 2009 → Dec 18 2009

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	12/15/09 → 12/18/09

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2009.5400596

Cite this

Li, N., Marden, J. R., & Shamma, J. S. (2009). Learning approaches to the Witsenhausen counterexample from a view of potential games. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 157-162). Article 05400596 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5400596

Li, Na ; Marden, Jason R. ; Shamma, Jeff S. / Learning approaches to the Witsenhausen counterexample from a view of potential games. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 157-162 (Proceedings of the IEEE Conference on Decision and Control).

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title = "Learning approaches to the Witsenhausen counterexample from a view of potential games",

abstract = "Since Witsenhausen put forward his remarkable counterexample in 1968, there have been many attempts to develop efficient methods for solving this non-convex functional optimization problem. However there are few methods designed from game theoretic perspectives. In this paper, after discretizing the Witsenhausen counterexample and re-writing the formulation in analytical expressions, we use fading memory JSFP with inertia, one learning approach in games, to search for better controllers from a view of potential games. We achieve a better solution than the previously known best one. Moreover, we show that the learning approaches are simple and automated and they are easy to extend for solving general functional optimization problems.",

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note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

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Li, N, Marden, JR & Shamma, JS 2009, Learning approaches to the Witsenhausen counterexample from a view of potential games. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 05400596, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 157-162, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 12/15/09. https://doi.org/10.1109/CDC.2009.5400596

Learning approaches to the Witsenhausen counterexample from a view of potential games. / Li, Na; Marden, Jason R.; Shamma, Jeff S.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 157-162 05400596 (Proceedings of the IEEE Conference on Decision and Control).

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

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AB - Since Witsenhausen put forward his remarkable counterexample in 1968, there have been many attempts to develop efficient methods for solving this non-convex functional optimization problem. However there are few methods designed from game theoretic perspectives. In this paper, after discretizing the Witsenhausen counterexample and re-writing the formulation in analytical expressions, we use fading memory JSFP with inertia, one learning approach in games, to search for better controllers from a view of potential games. We achieve a better solution than the previously known best one. Moreover, we show that the learning approaches are simple and automated and they are easy to extend for solving general functional optimization problems.

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BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

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Li N, Marden JR, Shamma JS. Learning approaches to the Witsenhausen counterexample from a view of potential games. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 157-162. 05400596. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5400596

Learning approaches to the Witsenhausen counterexample from a view of potential games

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