Prokaryotic evolutionary mechanisms accelerate learning

In 2006, Valiant introduced a variation to his celebrated PAC model to Biology, by which he wished to explain how such complex life mechanisms evolved in that short time by two simple mechanisms — random variation and natural selection. Soon after, several works extended and specialized his work to more specific processes. To the best of our knowledge, there is no such extension to the prokaryotic world, in which gene sharing is the prevailing mode of evolution. In this work we do the first step in this direction by extending the evolvability framework to accommodate horizontal gene transfer (HGT). Despite its computational equivalence to the basic evolvability model, we prove that under certain cases the new model allows an asymptotic acceleration in terms of the number of generations. This is done via a general reduction from parallel CSQ algorithm. As a demonstration of its learning power, we show that the concept class of conjunctions, a common concept class in the computational learning literature, can be learned by evolvability with HGT in constant number of generations.