eprintid: 10192390 rev_number: 6 eprint_status: archive userid: 699 dir: disk0/10/19/23/90 datestamp: 2024-05-16 11:18:24 lastmod: 2024-05-16 11:18:24 status_changed: 2024-05-16 11:18:24 type: proceedings_section metadata_visibility: show sword_depositor: 699 creators_name: Hellström, Fredrik creators_name: Guedj, Benjamin title: Comparing Comparators in Generalization Bounds ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 note: © The Authors 2024. Original content in this paper is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). abstract: We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training loss and the 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 Cramér 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. date: 2024 date_type: published publisher: PMLR (Proceedings of Machine Learning Research) official_url: https://proceedings.mlr.press/v238/hellstrom24a.html oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2275094 lyricists_name: Guedj, Benjamin lyricists_id: BGUED94 actors_name: Flynn, Bernadette actors_id: BFFLY94 actors_role: owner full_text_status: public pres_type: paper publication: AISTATS volume: 238 pagerange: 73-81 event_title: The 27th International Conference on Artificial Intelligence and Statistics book_title: Proceedings of The 27th International Conference on Artificial Intelligence and Statistics editors_name: Dasgupta, Sanjoy editors_name: Mandt, Stephan editors_name: Li, Yingzhen citation: Hellström, Fredrik; Guedj, Benjamin; (2024) Comparing Comparators in Generalization Bounds. In: Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen, (eds.) Proceedings of The 27th International Conference on Artificial Intelligence and Statistics. (pp. pp. 73-81). PMLR (Proceedings of Machine Learning Research) Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10192390/1/hellstrom24a.pdf