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