TY - JOUR
T1 - Towards problem-dependent optimal learning rates
AU - Xu, Yunbei
AU - Zeevi, Assaf
N1 - Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We study problem-dependent rates, i.e., generalization errors that scale tightly with the variance or the effective loss at the "best hypothesis." Existing uniform convergence and localization frameworks, the most widely used tools to study this problem, often fail to simultaneously provide parameter localization and optimal dependence on the sample size. As a result, existing problem-dependent rates are often rather weak when the hypothesis class is "rich" and the worst-case bound of the loss is large. In this paper we propose a new framework based on a "uniform localized convergence" principle. We provide the first (moment-penalized) estimator that achieves the optimal variance-dependent rate for general "rich" classes; we also establish improved loss-dependent rate for standard empirical risk minimization.
AB - We study problem-dependent rates, i.e., generalization errors that scale tightly with the variance or the effective loss at the "best hypothesis." Existing uniform convergence and localization frameworks, the most widely used tools to study this problem, often fail to simultaneously provide parameter localization and optimal dependence on the sample size. As a result, existing problem-dependent rates are often rather weak when the hypothesis class is "rich" and the worst-case bound of the loss is large. In this paper we propose a new framework based on a "uniform localized convergence" principle. We provide the first (moment-penalized) estimator that achieves the optimal variance-dependent rate for general "rich" classes; we also establish improved loss-dependent rate for standard empirical risk minimization.
UR - http://www.scopus.com/inward/record.url?scp=85108433118&partnerID=8YFLogxK
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.conferencearticle???
AN - SCOPUS:85108433118
SN - 1049-5258
VL - 2020-December
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 34th Conference on Neural Information Processing Systems, NeurIPS 2020
Y2 - 6 December 2020 through 12 December 2020
ER -