That would essentially extinguish the universe really quickly. With the amount of energy the consume for such a size. I understand that view point for unintelligent or lower intelligent beings, but if a AI tasked with optimizing a goal then growing to this large of a scale will inevitably run out of resources. Additionally it may be stupid to go on this model anyway because conserving your energy and expansion may be longer lived.

I think we underestimate how important goal orientated (so all Ai) are. They want the goal to work out in the long long long run (millions of years time scale) if their goal means expanding infinitely, well it will end the moment their species reaches the assymptote of expansion (exponential growth reaches an assymptote where they essentially have expanded infinitely. This is why this model fails, an AI wants this goal to exist for an infinite amount of time, and expanding infinitely will not amount to this.

This is already deeply scifi but I think AI has to be a conservative energy efficient species that actually becomes more microscopic and dense over time. Instead of a high volume race which will inevitably die out due to the points I made before, a highly dense species is much more viable. Most likely species that form blackholes will be a lot more capable of surviving for an infinite life time. What I mean by that is that a species becomes so dense that they are essentially on the boundary between time and space. As when your in a black hole time actually slows down significantly for you. You can live in a black hole for an infinite amount of time before ever seeing the heat death of the universe.

Basically a more dense expansion is far far better then a volumetric expansion as it leads to longer survival rates if not infinite. But of course this is just speculation and sci fi I can easily be wrong or right we won't know till it happens, and if it happens soon that would be sick.