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What do the no free lunch theorems assert?

  • A.No algorithm can be both accurate and interpretable at once
  • B.No algorithm outperforms all others averaged over all problems
  • C.No algorithm can learn anything at all from a finite data set
  • D.Every learning problem requires the same amount of computation

Answer: B

Averaged over every possible problem, all algorithms perform equally, so any algorithm's advantage comes from its assumptions matching the structure of the problems actually encountered. That is why choosing a method is choosing a set of assumptions rather than finding a universally best tool. Learning from finite data is certainly possible given assumptions, and computation and interpretability are separate matters. A theorem that forbids a universal solution redirects effort towards understanding the problem instead.

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