X Equestris
Maester
Throwing in a little GOT... Jaime is a villian, you don't push a kid out of a tower while banging your sis and not be a villain. Do we empathize with him? Sure, we might come to, and he might seek redemption in his own self-serving way, but calling him gray is a little off... or... if you want to call him gray, you must admit a character arc.
I'd say that Jaime is definitely on a redemptive arc by the point the books are at now.