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Abstract
This paper focuses on an Adaptive Cubic Regularisation (ARC) method for
approximating a secondorder critical point of a finite sum minimisation problem.
The variant presented belongs to the framework of Bellavia, Gurioli, Morinin
and Toint (2020): it employs random models with accuracy guaranteed with a
sufficiently large prefixed probability and deterministic inexact function
evaluations within a prescribed level of accuracy. Without assuming unbiased
estimators, the expected number of iterations is O( epsilon_1^{3/2} ) or O( \max[ epsilon_1^{3/2},epsilon_2^{3} ] ) when searching for a first or secondorder critical point, respectively, where epsilon_j is the jthorder tolerance. These results match the worstcase optimal complexity for the deterministic counterpart of the method.
approximating a secondorder critical point of a finite sum minimisation problem.
The variant presented belongs to the framework of Bellavia, Gurioli, Morinin
and Toint (2020): it employs random models with accuracy guaranteed with a
sufficiently large prefixed probability and deterministic inexact function
evaluations within a prescribed level of accuracy. Without assuming unbiased
estimators, the expected number of iterations is O( epsilon_1^{3/2} ) or O( \max[ epsilon_1^{3/2},epsilon_2^{3} ] ) when searching for a first or secondorder critical point, respectively, where epsilon_j is the jthorder tolerance. These results match the worstcase optimal complexity for the deterministic counterpart of the method.
Original language  English 

Publication status  Accepted/In press  2020 
Event  Thirtyseventh International Conference on Machine Learning: ICML2020  Duration: 13 Jul 2020 → 18 Jul 2020 
Conference
Conference  Thirtyseventh International Conference on Machine Learning 

Period  13/07/20 → 18/07/20 
Keywords
 Stochastic optimization
 Complexity theory
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Projects
 2 Active

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research
