What Is Important About the No Free Lunch Theorems?

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