A General Framework for the Practical Disintegration of PAC-Bayesian Bounds
This work addresses a bottleneck in generalization analysis for deterministic models, offering a more efficient and optimizable framework for researchers and practitioners in machine learning.
The paper tackles the issue of applying PAC-Bayesian bounds to deterministic models like neural networks by introducing new disintegrated bounds that provide guarantees for single hypotheses, eliminating the need for costly derandomization. It demonstrates significant practical improvements over state-of-the-art methods in neural network applications.
PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic models such as neural networks. As an alternative to this step, we introduce new PAC-Bayesian generalization bounds that have the originality to provide disintegrated bounds, i.e., they give guarantees over one single hypothesis instead of the usual averaged analysis. Our bounds are easily optimizable and can be used to design learning algorithms. We illustrate this behavior on neural networks, and we show a significant practical improvement over the state-of-the-art framework.