  The No Free Lunch theorems prove that under a uniform distribution over
induction problems (search problems or learning problems), all induction
algorithms perform equally. As I discuss in this chapter, the importance of the
theorems arises by using them to analyze scenarios involving {non-uniform}
distributions, and to compare different algorithms, without any assumption
about the distribution over problems at all. In particular, the theorems prove
that {anti}-cross-validation (choosing among a set of candidate algorithms
based on which has {worst} out-of-sample behavior) performs as well as
cross-validation, unless one makes an assumption -- which has never been
formalized -- about how the distribution over induction problems, on the one
hand, is related to the set of algorithms one is choosing among using
(anti-)cross validation, on the other. In addition, they establish strong
caveats concerning the significance of the many results in the literature which
establish the strength of a particular algorithm without assuming a particular
distribution. They also motivate a ``dictionary'' between supervised learning
and improve blackbox optimization, which allows one to ``translate'' techniques
from supervised learning into the domain of blackbox optimization, thereby
strengthening blackbox optimization algorithms. In addition to these topics, I
also briefly discuss their implications for philosophy of science.
