Expected Value Optimization

< Back to Projects

Expected Distance of Random Interior Point of an N-cube to its Nearest Face

This generalizes the problem of finding the expected value from a random point in a unit square to its nearest face.

View the Full Paper

You can view the full paper below or download it directly.

Abstract

This paper investigates the expected distance of random interior points to the nearest face in an n-dimensional hypercube, with applications to optimization algorithms in machine learning. We derive closed-form expressions for these distances and demonstrate how these insights can be applied to improve sampling strategies and convergence rates in stochastic optimization methods used for training neural networks.