# Accelerated gradient methods with absolute and relative noise in the gradient

arXiv: https://arxiv.org/abs/2102.02921 · HTML: https://mlsanity.com/paper/2102.02921/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2021.

## Built on by (most cited first, 2 of 2)

- [From Inexact Gradients to Byzantine Robustness: Acceleration and Optimization under Similarity](https://mlsanity.com/paper/2602.03329/) (2026)
- [Wall-Clock Complexity for Zeroth-Order Optimization with Tunable Oracle Fidelity](https://mlsanity.com/paper/2605.31346/) (2026)

## Abstract (arXiv)

In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities: absolute noise bounded by a constant, and relative noise proportional to the norm of the gradient. We investigate the accumulation of the errors in the convex and strongly convex settings with the main difference with most of the previous works being that the feasible set can be unbounded. The key to the latter is to prove a bound on the trajectory of the algorithm. We also give a stopping criterion for the algorithm and consider extensions to the cases of stochastic optimization and composite nonsmooth problems.