The power of first-order smooth optimization for black-box non-smooth problems

A Gasnikov, A Novitskii, V Novitskii… - arXiv preprint arXiv …, 2022 - arxiv.org
Gradient-free/zeroth-order methods for black-box convex optimization have been
extensively studied in the last decade with the main focus on oracle calls complexity. In this …

A Damped Newton Method Achieves Global and Local Quadratic Convergence Rate

S Hanzely, D Kamzolov… - Advances in …, 2022 - proceedings.neurips.cc
In this paper, we present the first stepsize schedule for Newton method resulting in fast
global and local convergence guarantees. In particular, we a) prove an $\mathcal O\left …

Cubic regularized subspace Newton for non-convex optimization

J Zhao, A Lucchi, N Doikov - arXiv preprint arXiv:2406.16666, 2024 - arxiv.org
This paper addresses the optimization problem of minimizing non-convex continuous
functions, which is relevant in the context of high-dimensional machine learning applications …

Advancing the lower bounds: An accelerated, stochastic, second-order method with optimal adaptation to inexactness

A Agafonov, D Kamzolov, A Gasnikov, A Kavis… - arXiv preprint arXiv …, 2023 - arxiv.org
We present a new accelerated stochastic second-order method that is robust to both
gradient and Hessian inexactness, which occurs typically in machine learning. We establish …

Hyperfast second-order local solvers for efficient statistically preconditioned distributed optimization

P Dvurechensky, D Kamzolov, A Lukashevich… - EURO Journal on …, 2022 - Elsevier
Statistical preconditioning enables fast methods for distributed large-scale empirical risk
minimization problems. In this approach, multiple worker nodes compute gradients in …

Improving Stochastic Cubic Newton with Momentum

EM Chayti, N Doikov, M Jaggi - arXiv preprint arXiv:2410.19644, 2024 - arxiv.org
We study stochastic second-order methods for solving general non-convex optimization
problems. We propose using a special version of momentum to stabilize the stochastic …

Acceleration exists! optimization problems when oracle can only compare objective function values

A Lobanov, A Gasnikov, A Krasnov - The Thirty-eighth Annual …, 2024 - openreview.net
Frequently, the burgeoning field of black-box optimization encounters challenges due to a
limited understanding of the mechanisms of the objective function. To address such …

A stochastic objective-function-free adaptive regularization method with optimal complexity

S Gratton, S Jerad, PL Toint - arXiv preprint arXiv:2407.08018, 2024 - arxiv.org
A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex
optimization is presented which never computes the objective-function value, but yet …

[PDF][PDF] Accelerated adaptive cubic regularized quasi-newton methods

D Kamzolov, K Ziu, A Agafonov… - arXiv preprint arXiv …, 2023 - researchgate.net
In this paper, we propose Cubic Regularized Quasi-Newton Methods for (strongly)
starconvex and Accelerated Cubic Regularized Quasi-Newton for convex optimization. The …

Exploiting Higher Order Derivatives in Convex Optimization Methods

D Kamzolov, A Gasnikov, P Dvurechensky… - Encyclopedia of …, 2023 - Springer
It is well known since the works of Newton [64] and Kantorovich [45] that the second-order
derivative of the objective function can be used in numerical algorithms for solving …