TY - GEN
T1 - Optimal and Adaptive Monteiro-Svaiter Acceleration
AU - Carmon, Yair
AU - Hausler, Danielle
AU - Jambulapati, Arun
AU - Jin, Yujia
AU - Sidford, Aaron
N1 - Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.
PY - 2022
Y1 - 2022
N2 - We develop a variant of the Monteiro-Svaiter (MS) acceleration framework that removes the need to solve an expensive implicit equation at every iteration. Consequently, for any p ≥ 2 we improve the complexity of convex optimization with Lipschitz pth derivative by a logarithmic factor, matching a lower bound. We also introduce an MS subproblem solver that requires no knowledge of problem parameters, and implement it as either a second- or first-order method via exact linear system solution or MinRes, respectively. On logistic regression our method outperforms previous second-order acceleration schemes, but under-performs Newton's method; simply iterating our first-order adaptive subproblem solver performs comparably to L-BFGS.
AB - We develop a variant of the Monteiro-Svaiter (MS) acceleration framework that removes the need to solve an expensive implicit equation at every iteration. Consequently, for any p ≥ 2 we improve the complexity of convex optimization with Lipschitz pth derivative by a logarithmic factor, matching a lower bound. We also introduce an MS subproblem solver that requires no knowledge of problem parameters, and implement it as either a second- or first-order method via exact linear system solution or MinRes, respectively. On logistic regression our method outperforms previous second-order acceleration schemes, but under-performs Newton's method; simply iterating our first-order adaptive subproblem solver performs comparably to L-BFGS.
UR - http://www.scopus.com/inward/record.url?scp=85162795092&partnerID=8YFLogxK
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AN - SCOPUS:85162795092
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
A2 - Koyejo, S.
A2 - Mohamed, S.
A2 - Agarwal, A.
A2 - Belgrave, D.
A2 - Cho, K.
A2 - Oh, A.
PB - Neural information processing systems foundation
T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Y2 - 28 November 2022 through 9 December 2022
ER -