AA Reg almost has to take Swift Anklets I think.
You dont have mines to put in between you and your opponent to defend yourself. And even if you have Blood of the Fallen, you are still going to get chewed up fast since you are still not going to have enough health to stand up to most DGs. Your only defense is speed. Its a really REALLY bad idea to allow the possibility of being slower than opposing DGs even before getting hit with slow skills as Reg if you dont have mines. With a Mines build you have more choices since you can basically defend yourself by putting mines between you and the other DG.
Plus, the one thing that AA Reg does really well in all stages of the game is chasing down the weak and finishing them (plus you are going to have to be good at this if you want kills because you dont have the burst damage to get quick kills). And that is going to require you to have a speed advantage also.
The exception to this is ntropy's suggestion. If you are going for a slow and control build, then you want Poisoned Dagger. But thats not really an AA Reg build since those builds usually use mines.