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Errors as a Means of Reducing Impulsive Food Choice
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Published on: June 5, 2016

Reinterpreting no free lunch.

Jon E Rowe1, M D Vose, Alden H Wright

  • 1School of Computer Science, The University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom. J.E.Rowe@cs.bham.ac.uk

Evolutionary Computation
|February 12, 2009
PubMed
Summary
This summary is machine-generated.

The "No Free Lunch" theorem (NFL) has been misunderstood; this paper clarifies its underlying symmetries. We present a set-theoretic NFL version applicable to arbitrary domains, revealing insights into deterministic and stochastic algorithms.

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Area of Science:

  • Theoretical Computer Science
  • Information Theory
  • Machine Learning Theory

Background:

  • The "No Free Lunch" theorem (NFL) is often discussed in terms of its algorithmic implications.
  • This perspective conflates the theorem's results with their specific applications.
  • This obscures the fundamental nature of the symmetries that underpin the NFL theorem.

Purpose of the Study:

  • To decouple the "No Free Lunch" theorem's results from their applications.
  • To clarify the inherent symmetries involved in the NFL theorem.
  • To establish a general, set-theoretic formulation of the NFL theorem.

Main Methods:

  • Developing a general set-theoretic framework for analyzing symmetries.
  • Abstracting the NFL theorem from specific algorithmic contexts.
  • Applying set theory to arbitrary domains and co-domains.

Main Results:

  • A general set-theoretic version of the "No Free Lunch" theorem is derived.
  • This formulation highlights the underlying symmetries more clearly.
  • The deterministic set-theoretic results offer insights applicable to stochastic algorithms.

Conclusions:

  • The NFL theorem's core lies in its symmetries, not just its results.
  • A set-theoretic approach provides a more general and powerful understanding.
  • This framework enhances the analysis of both deterministic and stochastic algorithms.