# Online Gradient Descent in Function Space

arXiv: https://arxiv.org/abs/1512.02394 · HTML: https://mlsanity.com/paper/1512.02394/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2015.

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

- [Fast Second-Order Online Kernel Learning through Incremental Matrix Sketching and Decomposition](https://mlsanity.com/paper/2410.11188/) (2024)

## Abstract (arXiv)

In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i.e. to solve optimization problems in an infinite dimensional space. On the other hand, online learning has the advantage of dealing with streaming examples, and better model a changing environ- ment. In this paper, we extend the celebrated online gradient descent algorithm to Hilbert spaces (function spaces), and analyze the convergence guarantee of the algorithm. Finally, we demonstrate that our algorithms can be useful in several important problems.