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Machine learning models trained by different optimization algorithms underdifferent data distributions can exhibit distinct generalization behaviors. Inthis paper, we analyze the generalization of models trained by noisy iterativealgorithms. We derive distribution-dependent generalization bounds byconnecting noisy iterative algorithms to additive noise channels found incommunication and information theory. Our generalization bounds shed light onseveral applications, including differentially private stochastic gradientdescent (DP-SGD), federated learning, and stochastic gradient Langevin dynamics(SGLD). We demonstrate our bounds through numerical experiments, showing thatthey can help understand recent empirical observations of the generalizationphenomena of neural networks.

Generalization Bounds for Noisy Iterative Algorithms Using Properties of Additive Noise Channels