Is it possible that, at some time in the future, AIs will be able to initiatively develop themselves, rather than passively being developed by humanity?
Humans might create somewhere in the future a so-called ultraintelligent machine, a machine that can surpass all intellectual activities by any human. This would be the last invention man would need to do, since this machine is better in inventing machines than humans are (since that is an intellectual activity). Also, since humans can create machines as good as the ultraintelligent machine, this machine can create better machines, which in turn can create better machines, etcetera. This is known as the Intelligence explosion, and it is also called recursive self-improvement.
The existence, let alone the development, if an ultraintelligent machine is still hypothetical. We are nowhere close to creating an ultraintelligent machine.
It depends what you mean by 'develop themselves' - in a rather limited sense, an online machine learning approach such as Genetic Algorithms 'develops itself' to provide better solutions.
There is already a theoretical model that represents the ultimate concept of development: Juergen Schmidhuber's Goedel Machine is constructed so as to self-modify when it can prove that this modification is optimal.