Comparing Comparators in Generalization Bounds

Autor:	Hellström, Fredrik, Guedj, Benjamin
Rok vydání:	2023
Předmět:	Computer Science - Machine Learning Computer Science - Information Theory Mathematics - Statistics Theory Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training and population loss. The bounds hold under the assumption that the cumulant-generating function (CGF) of the comparator is upper-bounded by the corresponding CGF within a family of bounding distributions. We show that the tightest possible bound is obtained with the comparator being the convex conjugate of the CGF of the bounding distribution, also known as the Cram\'er function. This conclusion applies more broadly to generalization bounds with a similar structure. This confirms the near-optimality of known bounds for bounded and sub-Gaussian losses and leads to novel bounds under other bounding distributions. Comment: AISTATS 2024
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.10534 Zobrazit plný text záznamu View this record from Arxiv