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Previous research on PAC-Bayes learning theory has focused extensively onestablishing tight upper bounds for test errors. A recently proposed trainingprocedure called PAC-Bayes training, updates the model toward minimizing thesebounds. Although this approach is theoretically sound, in practice, it has notachieved 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 andmay need a search over priors with additional datasets, which limits theirbroader applicability. In this paper, we introduce a new PAC-Bayes trainingalgorithm with improved performance and reduced reliance on prior tuning. Thisis achieved by establishing a new PAC-Bayes bound for unbounded loss and atheoretically grounded approach that involves jointly training the prior andposterior using the same dataset. Our comprehensive evaluations across variousclassification tasks and neural network architectures demonstrate that theproposed method not only outperforms existing PAC-Bayes training algorithms butalso approximately matches the test accuracy of ERM that is optimized bySGD/Adam using various regularization methods with optimal hyperparameters.

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