Improving Generalization of Complex Models under Unbounded Loss Using PAC-Bayes Bounds
This addresses a limitation in machine learning theory for researchers and practitioners by improving the practical applicability of PAC-Bayes methods, though it is incremental as it builds on existing PAC-Bayes frameworks.
The paper tackles the problem of PAC-Bayes training algorithms underperforming compared to empirical risk minimization (ERM) and requiring bounded loss functions, by introducing a new algorithm that uses a PAC-Bayes bound for unbounded loss and joint training of prior and posterior, achieving test accuracy approximately matching optimized ERM.
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.