5.4. Microchoice discussion

Microchoice bounds can be used in practice and do yield results comparable with holdout set based techniques (see figure . 12.3.5 and the surrounding section for details). There are two significant insights which the microchoice bounds provide.

1. The “cost” of choices is made very explicit. The cost of a choice (in terms of sample complexity) is the log of the number of choices.
2. It is possible to improve upon the Occam’s Razor Bound (theorem 4.6.1) by using information from the sample set to infer properties (such as the choice tree) of the distribution $D$. This can be done without any explicit knowledge of the distribution $D$.