Stopping rules for accelerated gradient methods with additive noise in gradient
- Vasin, Artem
- Gasnikov, Alexander
- Spokoiny, Vladimir
2020 Mathematics Subject Classification
- 90C30 90C25 68Q25
- Accelerated methods, inexact gradient, stopping rule, inverse problems
In this article, we investigate an accelerated first-order method, namely, the method of similar triangles, which is optimal in the class of convex (strongly convex) problems with a Lipschitz gradient. The paper considers a model of additive noise in a gradient and a Euclidean prox- structure for not necessarily bounded sets. Convergence estimates are obtained in the case of strong convexity and its absence, and a stopping criterion is proposed for not strongly convex problems.