Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks

Felix Biggs; Benjamin Guedj

doi:10.3390/e23101280

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arXiv · 2006.12228

Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks

Felix Biggs·Benjamin Guedj

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Abstract

We make three related contributions motivated by the challenge of training stochastic neural networks, particularly in a PAC-Bayesian setting: (1) we show how averaging over an ensemble of stochastic neural networks enables a new class of \emph{partially-aggregated} estimators; (2) we show that these lead to provably lower-variance gradient estimates for non-differentiable signed-output networks; (3) we reformulate a PAC-Bayesian bound for these networks to derive a directly optimisable, differentiable objective and a generalisation guarantee, without using a surrogate loss or loosening the bound. This bound is twice as tight as that of Letarte et al. (2019) on a similar network type. We show empirically that these innovations make training easier and lead to competitive guarantees.

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Felix Biggs, Benjamin Guedj. 2020-06-22. Differentiable PAC-Bayes Objectives with Partially Aggregated Neural Networks. https://doi.org/10.3390/e23101280

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