# Proximal gradient methods with inexact oracle of degree q for composite optimization

arXiv: https://arxiv.org/abs/2401.10624 · HTML: https://mlsanity.com/paper/2401.10624/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2024.

## Built on by (most cited first, 1 of 1)

- [On the Convergence of Stochastic Gradient Descent with Perturbed Forward-Backward Passes](https://mlsanity.com/paper/2602.20646/) (2026)

## Abstract (arXiv)

We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.