InterJournal Complex Systems, 927
Status: Accepted
Manuscript Number: [927]
Submission Date: 2004
Experimental tests of product distribution theory
Author(s): David H. Wolpert ,William Macready

Subject(s): CX.0

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Abstract:

This paper presents product distribution theory, a powerful new framework for analyzing and controlling distributed systems. There are many ways to motivate product distribution theory. It is the information-theoretic extension of conventional full-rationality game theory, to the case of bounded rational players. It can also be viewed as a modification of the Lagrangian formulation of statistical physics in which the variables of the system are required to be independent. It also provides an alternative to conventional optimization, in which rather than use probability distributions to help in a search for an optimal point in a space, one reformulates the problem as a search for an optimal probability distribution over that space. The final motivation of the framework is as the way to optimally approximate a provided probability distribution with a lower-dimensional distribution. This framework has potential applications in many engineering domains: (constrained) optimization, distributed adaptive control of multi-agent systems, sampling of probability densities, density estimation, numerical integration, information-theoretic bounded, and reinforcement learning. It also has many purely scientific applications, for example in the sciences of rational game theory, population biology, and management theory. After introducing product distribution theory this paper presents computer experiments validating its utility for several of the engineering applications listed above.

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