A General Framework for the Practical Disintegration of PAC-Bayesian Bounds

TL;DR

This paper introduces a new framework for PAC-Bayesian bounds that disintegrate the usual averaged guarantees, enabling more practical and tighter generalization bounds for neural networks and other models.

Contribution

It proposes a novel disintegrated PAC-Bayesian bound that applies to individual hypotheses, simplifying optimization and improving practical performance.

Findings

Significant improvement over existing PAC-Bayesian bounds for neural networks.

Bounds are easily optimizable and can guide the design of learning algorithms.

Demonstrated practical benefits on neural network models.

Abstract

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.