Stochastic Subspace Descent

Understand

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and machine learning problems.

• The basic algorithm projects the gradient onto a random subspace at each iteration, similar to coordinate descent but without restricting directional derivatives to be along the axes.
• This algorithm is previously known but we provide new analysis.
• We also extend the popular SVRG method to this framework but without requiring that the objective function be written as a finite sum.