I have found that peat mixes almost always seem to promote algae blooms for some reason, and lowers the pH quite a bit. The Aldrovanda does best with some clay and leaf litter with a neutral pH=7.0.
I find that algae is present, but not in long strands. It almost always forms near U. inflata, but never smothers any plants. Our water here is quite hard and alkaline... the peat was put in mostly to buffer the water back to a neutral pH. The outdoor setup has an inch layer of our soil... which coincidentally is adobe clay. That tank is always devoid of algae.
I should also mention that Aldrovanda has a horrific winter fatality rate, up to 95%...
In the summer, I will probably reintroduce some Aldrovanda from my indoor stock back outdoors. I have a feeling that I won't find any there come spring, but only time will tell.