Probability Collectives

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Synopsis

Probability Collectives is a broad framework for analyzing and controlling distributed systems. It is based on deep formal connections relating game theory, statistical physics, and distributed control/optimization.

This site provides some papers detailing the theory as well as applications of Probability Collectives.

In some cases the papers below are revised and corrected versions of the originals which appeared in the references listed.

Dissertations

  • Probability Collectives for aerospace systems.
    Includes theory and implementation of approach, and applies it to a range of optimization problems and experiments in distributed flight control.
    Stefan Bieniawski, Distributed Optimization and Flight Control Using Collectives, Stanford University, September 2005. [Defense Presentation] [Dissertation]

    Theory Papers

  • Theory introduction
    David H. Wolpert, Information Theory — The Bridge Connecting Bounded Rational Game Theory and Statistical Physics
    In Complex Engineering Systems, edited by Yaneer Bar-Yam and Dan Braha, Perseus books, in print. [pdf] [ps]

  • Presentation which introduces the theory
    David H. Wolpert, Bounded Rationality and Statistical Physics.
    NASA-ARC-03-097. [pdf]

  • Highlighting the connection to game theory
    David H. Wolpert, What Information Theory says about Best Response and about Binding Contracts
    In Proceeding of WEHIA 2004, edited by Akira Namatame et al., Springer-Verlag, in print. [ps]

  • Theory applied to distributed control
    David H. Wolpert and Stefan Bieniawski, Distributed Control by Lagrangian Steepest Descent
    In Proceeding of the Conference of Decision and Control, 2004. [pdf] [ps]

  • Theory applied to reinforcement learning
    David H. Wolpert and Stefan Bieniawski, Distributed Adaptive Control: Beyond Single-Instant, Discrete Variables
    MSRAS 2004, In Advances in Soft Computing, edited by Andrzej Jankowski, Andrzej Skowron, and Marcin Szczuka, Springer-Verlag, 2004. [ps]

  • Finding bounded rational equilibria
    David H. Wolpert, Finding Bounded Rational Equilibria, Part I : Interative Focusing
    In Proceeding of the Eleventh International Symposium on Dynamic Games and Applications, Tucson Arizona,December 18-21, 2004.
    [Part 1] [Part 2 (draft)]

  • Example of semi-coordinate transformations
    Stephen Airiau and David H. Wolpert, Product Distribution Theory and Semi-Coordinate Transformations
    Unpublished. [pdf]

    Application Papers

  • Comparison with Genetic Algorithms
    Chien-Feng Huang, Stefan Bieniawski, Charlie E. M. Strauss, and David H. Wolpert, A Comparative Study of Probability Collectives Based Multiagent Systems and Genetic Algorithms
    Submitted to GECCO 2005. [pdf]

  • Optimization
    Stefan Bieniawski, David H. Wolpert, and Ilan Kroo, Discrete, Continuous, and Constrained Optimization Using Collectives
    AIAA Paper 2004-4580, Presented at the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, August 30-September 1, 2004. [pdf]

  • Theory validation and techniques to account for unknown form of the world utility
    Chiu Fan Lee and David H. Wolpert, Product distribution theory for control of multi-agent systems
    In Proceedings of the Third International Joint Conference on Autonomous Agents and Multi-Agent Systems, New York, NY, July 19-23, 2004. [pdf]

  • Comparisons with distributed reinforcement learning
    Stefan Bieniawski and David H. Wolpert, Adaptive, distributed control of constrained multi-agent systems
    In Proceedings of the Third International Joint Conference on Autonomous Agents and Multi-Agent Systems, New York, NY, July 19-23, 2004. [pdf] [poster]

  • Satisfiability (k-Sat), also highlighting mixture models
    William Macready and David H. Wolpert, Distributed Optimization
    Presented at the International Conference on Complex Systems, Boston, MA, May 16-21, 2004. [pdf] [ps]

  • Metropolis Hastings sampling
    David H. Wolpert and Chiu Fan Lee, Adaptive Metropolis Sampling with Product Distributions
    Presented at the International Conference on Complex Systems, Boston, MA, May 16-21, 2004. [pdf] [ps]

  • Comparisons with Serial and Parallel Brouwer
    Stefan Bieniawski and David H. Wolpert, Product Distributions for Distributed Optimization
    Presented at the International Conference on Complex Systems, Boston, MA, May 16-21, 2004. [pdf] [ps]

  • Aircraft routing
    Nicolas E. Antoine, Stefan Bieniawski, David H. Wolpert, and Ilan Kroo, Fleet Assignement Using Collective Intelligence
    AIAA Paper 2004-0622, Presented at 42nd AIAA Aerospace Sciences Meeting, Reno, NV, January 5-8, 2004. [pdf] [extended version]

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    Last update February 15,2005
    by Stefan Bieniawski