PRISMA: PRoximal Iterative SMoothing Algorithm
This incremental improvement addresses optimization challenges in machine learning applications such as clustering and sparse inverse covariance selection.
The authors tackled the problem of minimizing convex objectives with smooth and non-smooth components, common in tasks like matrix completion and robust PCA, by proposing a novel optimization algorithm that uses a time-variant smoothing strategy to achieve a guarantee independent of iteration count or domain bounds.
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz part, and a simple non-smooth non-Lipschitz part. We use a time variant smoothing strategy that allows us to obtain a guarantee that does not depend on knowing in advance the total number of iterations nor a bound on the domain.