?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Comparing+Comparators+in+Generalization+Bounds&rft.creator=Hellstr%C3%B6m%2C+Fredrik&rft.creator=Guedj%2C+Benjamin&rft.description=We+derive+generic+information-theoretic+and+PAC-Bayesian+generalization+bounds+involving+an+arbitrary+convex+comparator+function%2C+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%2C+also+known+as+the+Cram%C3%A9r+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.&rft.publisher=PMLR+(Proceedings+of+Machine+Learning+Research)&rft.contributor=Dasgupta%2C+Sanjoy&rft.contributor=Mandt%2C+Stephan&rft.contributor=Li%2C+Yingzhen&rft.date=2024&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A+Dasgupta%2C+Sanjoy+and+Mandt%2C+Stephan+and+Li%2C+Yingzhen%2C+(eds.)+Proceedings+of+The+27th+International+Conference+on+Artificial+Intelligence+and+Statistics.++(pp.+pp.+73-81).++PMLR+(Proceedings+of+Machine+Learning+Research)+(2024)+++++&rft.format=application%2Fpdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10192390%2F1%2Fhellstrom24a.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10192390%2F&rft.rights=open