In principle a thousand different deep learning models could all train simultaneously on a thousand different robot experience feeds.. but not 1 to 1, but instead 1 to many.. each neural net training on data from dozens or hundreds of the robots at the same time, and different neural nets sharing those feeds for their own rounds of training.
Then of course all of the input data paired with outputs tested and further inputs as ground truth to predictions can be recorded for continued training sessions after the fact.