The Deep Bootstrap Framework: Good Online Learners are Good Offline Generalizers
This framework offers a new perspective for understanding generalization in deep learning, potentially simplifying the problem for researchers in the field.
This paper introduces a framework that decomposes test error into an Ideal World test error and a gap between the Real and Ideal Worlds. They provide empirical evidence that this gap can be small in deep learning, suggesting that generalization in offline learning can be reduced to optimization in online learning.
We propose a new framework for reasoning about generalization in deep learning. The core idea is to couple the Real World, where optimizers take stochastic gradient steps on the empirical loss, to an Ideal World, where optimizers take steps on the population loss. This leads to an alternate decomposition of test error into: (1) the Ideal World test error plus (2) the gap between the two worlds. If the gap (2) is universally small, this reduces the problem of generalization in offline learning to the problem of optimization in online learning. We then give empirical evidence that this gap between worlds can be small in realistic deep learning settings, in particular supervised image classification. For example, CNNs generalize better than MLPs on image distributions in the Real World, but this is "because" they optimize faster on the population loss in the Ideal World. This suggests our framework is a useful tool for understanding generalization in deep learning, and lays a foundation for future research in the area.