# Characterization of Convex Objective Functions and Optimal Expected Convergence Rates for SGD

arXiv: https://arxiv.org/abs/1810.04100 · HTML: https://mlsanity.com/paper/1810.04100/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2018.

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

- [Gradient Descent-Type Methods: Background and Simple Unified Convergence Analysis](https://mlsanity.com/paper/2212.09413/) (2022)

## Abstract (arXiv)

We study Stochastic Gradient Descent (SGD) with diminishing step sizes for convex objective functions. We introduce a definitional framework and theory that defines and characterizes a core property, called curvature, of convex objective functions. In terms of curvature we can derive a new inequality that can be used to compute an optimal sequence of diminishing step sizes by solving a differential equation. Our exact solutions confirm known results in literature and allows us to fully characterize a new regularizer with its corresponding expected convergence rates.