Second-Order Methods with Cubic Regularization Under Inexact Information

Abstract

In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these methods and show the explicit dependence of the rate of convergence on the problem parameters. While the complexity bounds of our presented algorithms are theoretically worse than those of their exact counterparts, they are at least as good as those of the optimal first-order methods. Our numerical experiments also show that using inexact Hessians can significantly speed up the algorithms in practice.

References in corpus (2)

• Convergence rates of sub-sampled Newton methods
• Sub-sampled Newton Methods with Non-uniform Sampling

Cited by in corpus (9)

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• Randomized Block Cubic Newton Method
• Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models
• A Note on Inexact Condition for Cubic Regularized Newton's Method
• Inexact Proximal Cubic Regularized Newton Methods for Convex Optimization
• A Distributed Cubic-Regularized Newton Method for Smooth Convex Optimization over Networks
• A Unified Adaptive Tensor Approximation Scheme to Accelerate Composite Convex Optimization
• SingCubic: Cyclic Incremental Newton-type Gradient Descent with Cubic Regularization for Non-Convex Optimization