Most direct inject engines will have this problem due to carbon build on the intake valves. This is mainly caused by PCV vapers. The generation of fuel injection prior to direct injection sprayed fuel from the manifold side thus helping to clean the intake valves. That said I have found that using a product made by Chevron called Techron, helps with a cleaner and more complete combustion process and will clean dirty valves. I have also stopped using “cheep” lesser named brands of gasoline and these two things have relieved the poor idle problem. I also would recommend using a synthetic oil as they are less prone to vaporizing, helping to reduce the excessive crankcase vapers in the first place!
There is also a product from Gunk that is sprayed into the intake track directly while the engine is running, this cleans the intake runners and the intake valves directly!
I am not stating this to be the cure for all poor idle problems, but it has worked for me.
My process was:
Mobil1 5w30 oil change
Clean throttle body
Add 1 bottle of Techron to the recommended amount of fuel
Fill tank with top name brand fuel
Drive hard and put up wet! Lol
You have to admit that our cars are mostly luxury cars and are not driven very hard if at all, this in and of itself will contribute to the the carbon build up problem.
I have done the Techron additive every month and a half and my problem is gone!