Interestingly enough, that's exactly one of the constraints that our little robot will face when its launched into space to land on an ocean of methane on Titan. Bandwidth of information beamed long distances through space is at a premium, so one of the most important jobs of the Planetary Lake Lander Project is to teach the rover how to think for its self. It cant be phoning home to ask questions about whether or not to take a picture, collect a sample, or track an interesting incident.
Heres an interesting blog post by Tom Kerwick on how bandwidth limitation is driving research in Artificial Intelligence.