# The Search direction Correction makes first-order methods faster

arXiv: https://arxiv.org/abs/1905.06507 · HTML: https://mlsanity.com/paper/1905.06507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2019.

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

- [Don't be so Monotone: Relaxing Stochastic Line Search in Over-Parameterized Models](https://mlsanity.com/paper/2306.12747/) (2023)

## Abstract (arXiv)

The so-called fast inertial relaxation engine is a first-order method for unconstrained smooth optimization problems. It updates the search direction by a linear combination of the past search direction, the current gradient and the normalized gradient direction. We explore more general combination rules and call this generalized technique as the search direction correction (SDC). SDC is extended to composite and stochastic optimization problems as well. Deriving from a second-order ODE, we propose a fast inertial search direction correction (FISC) algorithm as an example of methods with SDC. We prove the O(k-2) convergence rate of FISC for convex optimization problems. Numerical results on sparse optimization, logistic regression as well as deep learning demonstrate that our proposed methods are quite competitive to other state-of-the-art first-order algorithms.