A Continuous-time Stochastic Gradient Descent Method for Continuous Data

Understand

Optimization problems with continuous data appear in, e.g., robust machine learning, functional data analysis, and variational inference.

• Here, the target function is given as an integral over a family of (continuously) indexed target functions - integrated with respect to a probability measure.
• Such problems can often be solved by stochastic optimization methods: performing optimization steps with respect to the indexed target function with randomly switched indices.
• In this work, we study a continuous-time variant of the stochastic gradient descent algorithm for optimization problems with continuous data.