Broad Area Colloquium For AI-Geometry-Graphics-Robotics-Vision
Probability Collectives and Supervised Learning
David H. Wolpert
May 22, 2006, 4:15PM
There are two major fields that analyze distributed systems:
statistical physics and game theory. These fields can be re-expressed
in a way that makes them mathematically identical. Doing so allows
us to combine techniques from them, producing a hybrid formalism.
That hybrid is called Probability Collectives (PC).
As borne out by numerous experiments, PC is particularly well-suited
to black-box optimization and associated problems in distributed
control. The core idea is that rather than directly optimize a
variable of interest x, often it is preferable to optimize an
associated probability distribution, P(x). That optimization can be
done either via Monte Carlo Optimization (MCO) or, under certain
circumstances, in closed form.
Recently it was realized that one can map MCO into a supervised
machine learning problem. This means that all the powerful techniques
of supervised learning can be used to improve MCO. As a special case,
those techniques can be used to improve the optimization of P(x) in a
PC-based optimizer. In this way the techniques of supervised learning
can be leveraged to improve black-box optimization and distributed
In this talk I review PC. I also illustrate the identity between MCO
and supervised learning using PC. In particular, I present results
showing how cross-validation can be used to adaptively set an
annealing schedule for the optimization of P(x), and to adaptively
modify the complexity of P(x). I also illustrate the benefit of
bagging in PC.
About the Speaker
David Wolpert received degrees in physics from the University of
California, Santa Barbara, and from Princeton University. He is
currently a Senior Computer Scientist at NASA and a consulting
professor at Stanford. He was formerly head of a data mining group at
IBM Almaden Research and a Postdoc at the Santa Fe Institute.
His work primarilly concerns how to design collectives of complex
adaptive agents to achieve a global goal (i.e., distributed control
and/or optimization). Other work investigates the bounds on
computation that hold in broad classes of physical universes, and the
use of self-dissimilarity as a complexity measure. He also works on
extending game theory to sub-rational games using techniques from
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