From what I've read in DANDR eating less than 20 grams of carbs has no advantage over eating 20 grams... and many people on this forum have indicated that they lost more quickly by eating more carbs... not alot more carbs, and all from good sources, but if you aren't eating enough in total, you could have problems from your body thinking it's starving. This can really impede weight loss...
I would suggest going totally by the book for induction, no sweeteners at all for the first two weeks... and then you can experiment from there, to see what your body will tolerate and what it won't.