eprintid: 10083912 rev_number: 35 eprint_status: archive userid: 608 dir: disk0/10/08/39/12 datestamp: 2019-10-30 15:22:46 lastmod: 2022-04-20 12:08:35 status_changed: 2019-10-30 15:22:46 type: article metadata_visibility: show creators_name: Guedj, B creators_name: Pujol, L title: Still no free lunches: the price to pay for tighter PAC-Bayes bounds ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 keywords: statistical learning theory; PAC-Bayes theory; no free lunch theorems note: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. abstract: “No free lunch” results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling, which is more or less realistic for a given problem. Some models are “expensive” (strong assumptions, such as sub-Gaussian tails), others are “cheap” (simply finite variance). As it is well known, the more you pay, the more you get: in other words, the most expensive models yield the more interesting bounds. Recent advances in robust statistics have investigated procedures to obtain tight bounds while keeping the cost of assumptions minimal. The present paper explores and exhibits what the limits are for obtaining tight probably approximately correct (PAC)-Bayes bounds in a robust setting for cheap models. date: 2021-11-18 official_url: https://doi.org/10.3390/e23111529 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1708791 doi: 10.3390/e23111529 lyricists_name: Guedj, Benjamin lyricists_id: BGUED94 actors_name: Guedj, Benjamin actors_id: BGUED94 actors_role: owner full_text_status: public publication: Entropy volume: 23 number: 11 article_number: 1529 citation: Guedj, B; Pujol, L; (2021) Still no free lunches: the price to pay for tighter PAC-Bayes bounds. Entropy , 23 (11) , Article 1529. 10.3390/e23111529 <https://doi.org/10.3390/e23111529>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10083912/1/entropy-23-01529-v2.pdf