TY - JOUR
T1 - RECAPP
T2 - 39th International Conference on Machine Learning, ICML 2022
AU - Carmon, Yair
AU - Jambulapati, Arun
AU - Jin, Yujia
AU - Sidford, Aaron
N1 - Publisher Copyright:
Copyright © 2022 by the author(s)
PY - 2022
Y1 - 2022
N2 - The accelerated proximal point algorithm (APPA), also known as “Catalyst”, is a well-established reduction from convex optimization to approximate proximal point computation (i.e., regularized minimization). This reduction is conceptually elegant and yields strong convergence rate guarantees. However, these rates feature an extraneous logarithmic term arising from the need to compute each proximal point to high accuracy. In this work, we propose a novel Relaxed Error Criterion for Accelerated Proximal Point (RECAPP) that eliminates the need for high accuracy subproblem solutions. We apply RECAPP to two canonical problems: finite-sum and max-structured minimization. For finite-sum problems, we match the best known complexity, previously obtained by carefully-designed problem-specific algorithms. For minimizing maxy f(x, y) where f is convex in x and strongly-concave in y, we improve on the best known (Catalyst-based) bound by a logarithmic factor.
AB - The accelerated proximal point algorithm (APPA), also known as “Catalyst”, is a well-established reduction from convex optimization to approximate proximal point computation (i.e., regularized minimization). This reduction is conceptually elegant and yields strong convergence rate guarantees. However, these rates feature an extraneous logarithmic term arising from the need to compute each proximal point to high accuracy. In this work, we propose a novel Relaxed Error Criterion for Accelerated Proximal Point (RECAPP) that eliminates the need for high accuracy subproblem solutions. We apply RECAPP to two canonical problems: finite-sum and max-structured minimization. For finite-sum problems, we match the best known complexity, previously obtained by carefully-designed problem-specific algorithms. For minimizing maxy f(x, y) where f is convex in x and strongly-concave in y, we improve on the best known (Catalyst-based) bound by a logarithmic factor.
UR - http://www.scopus.com/inward/record.url?scp=85137222312&partnerID=8YFLogxK
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AN - SCOPUS:85137222312
SN - 2640-3498
VL - 162
SP - 2658
EP - 2685
JO - Proceedings of Machine Learning Research
JF - Proceedings of Machine Learning Research
Y2 - 17 July 2022 through 23 July 2022
ER -