In the last blog post, we alluded to the No-Free-Lunch (NFL) theorems for search and optimization. While NFL theorems are criminally misunderstood and misrepresented in the service of crude generalizations intended to make a point, I intend to deploy a crude NFL generalization to make just such a point.
You see, NFL theorems (roughly) state that given a universe of problem sets where an algorithm’s goal is to learn a function that maps a set of input data X to a set of target labels Y, for any subset of problems where algorithm A outperforms algorithm B, there will be a subset of problems where B outperforms A. In fact, averaging their results over the space of all possible problems, the performance of algorithms A and B will be the same.
With some hand waving, we can construct an NFL theorem for the cybersecurity domain: Over the set of all possible attack vectors that could be employed by a hacker, no single detection algorithm can outperform all others across the full spectrum of attacks.