# Potential-Function Proofs for First-Order Methods

arXiv: https://arxiv.org/abs/1712.04581 · HTML: https://mlsanity.com/paper/1712.04581/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2017.

## Built on by (most cited first, 4 of 4)

- [From Gradient Flow on Population Loss to Learning with Stochastic Gradient Descent](https://mlsanity.com/paper/2210.06705/) (2022)
- [Stacking as Accelerated Gradient Descent](https://mlsanity.com/paper/2403.04978/) (2024)
- [A Class of Accelerated Fixed-Point-Based Methods with Delayed Inexact Oracles and Its Applications](https://mlsanity.com/paper/2512.13547/) (2025)
- [Exact information accounting for SGD methods](https://mlsanity.com/paper/2610.00446/) (2026)

## Abstract (arXiv)

This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.