Online Gradient Descent in Function Space

Understand

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.