Improving Generalization of Complex Models under Unbounded Loss Using PAC-Bayes Bounds

TL;DR

This paper introduces a new PAC-Bayes training algorithm that effectively handles unbounded loss functions, jointly trains prior and posterior, and achieves test accuracies comparable to traditional empirical risk minimization methods.

Contribution

It presents a novel PAC-Bayes bound for unbounded loss and a training procedure that jointly optimizes prior and posterior without extensive prior tuning.

Findings

Outperforms existing PAC-Bayes algorithms in various tasks.

Achieves test accuracy close to ERM with optimal regularization.

Demonstrates effectiveness across multiple neural network architectures.

Abstract

Previous research on PAC-Bayes learning theory has focused extensively on establishing tight upper bounds for test errors. A recently proposed training procedure called PAC-Bayes training, updates the model toward minimizing these bounds. Although this approach is theoretically sound, in practice, it has not achieved a test error as low as those obtained by empirical risk minimization (ERM) with carefully tuned regularization hyperparameters. Additionally, existing PAC-Bayes training algorithms often require bounded loss functions and may need a search over priors with additional datasets, which limits their broader applicability. In this paper, we introduce a new PAC-Bayes training algorithm with improved performance and reduced reliance on prior tuning. This is achieved by establishing a new PAC-Bayes bound for unbounded loss and a theoretically grounded approach that involves jointly training the prior and posterior using the same dataset. Our comprehensive evaluations across various classification tasks and neural network architectures demonstrate that the proposed method not only outperforms existing PAC-Bayes training algorithms but also approximately matches the test accuracy of ERM that is optimized by SGD/Adam using various regularization methods with optimal hyperparameters.