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John_Maxwell_IV comments on To reduce astronomical waste: take your time, then go very fast - Less Wrong
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Interesting stuff. It might be worth noting that by colonizing a few galaxies early on, you would gain increased research capacity with which to improve the way you colonize the rest of them. So the problem might be a bit more complicated.
If you're going really fast, there's only limited time for someone to research speed upgrades before you get too far away to ever get caught (cosmic expansion).
But it is slightly more complicated, as cosmic expansion robs you of speed as you hurtle. So there may be an argument to stop and re-accelerate at some point.