I am not aware of any self-improving compiler, but then again I am not much of a compiler-guy.
Is there ANY self-improving compiler out there?
Not yet practically implemented, to my knowledge, but yes, the theory is there:
While it is true that compilers can improve code without human interference, however, the claim that "compilers are self-improving" is rather dubious. These "improvements" that compilers make are merely based on a set of rules that are written by humans (cyborgs anyone?). So the answer to your question is : No.
On a side note, if there was anything like a self improving compiler, we'd know... first the thing would improve the language, then its own code and finally, it would modify its code to become a virus and make all developers use it... and then finally we'd have one of those classic computer-versus-humans-last-hope-for-humanity kind of things... so ... No.