# Convergence rates for the stochastic gradient descent method for non-convex objective functions

## TL;DR

This paper establishes local convergence and rate estimates for stochastic gradient descent on non-convex functions, relevant to machine learning applications, expanding understanding beyond convex scenarios.

## Contribution

It provides the first local convergence and rate results for SGD on non-convex, non-globally convex functions, applicable in machine learning.

## Key findings

- Proves local convergence to minima for non-convex functions.
- Provides estimates on the rate of convergence.
- Applicable to simple objective functions in machine learning.

## Abstract

We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions. In particular, the results are applicable to simple objective functions arising in machine learning.