This is what worked for me for this error:
Go to My Documents, Battlefield 4, settings and delete the following 3 files: PROFSAVE, PROFSAVE_header, PROFSAVE_profile
NOTE: This will reset all of your ingame settings to their default values
After that you can launch the game, but DONT TOUCH THE GRAPHICS QUALITY SETTINGS. LEAVE THEM TO AUTO (You can change any other settings to your liking). This is extremely important, it's the reason we deleted the files in the first place. Somehow changing the quality to auto in-game doesn't work, you have to delete the files.
I haven't had a single directx error window after this. I've had a few crashes, but I think they're mostly server side.
The first time i removed my files it worked, but when the map changes the directx error comes back...
