Online Gradient Descent in Function Space
This work addresses optimization in function spaces for machine learning and operations research, offering a method to handle streaming data in changing environments.
The authors tackled the problem of optimizing functions in infinite-dimensional spaces by extending online gradient descent to Hilbert spaces, and they provided convergence guarantees for the algorithm.
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.