PRISMA: PRoximal Iterative SMoothing Algorithm

TL;DR

PRISMA is a new optimization algorithm designed for convex problems with complex structure, employing a time-variant smoothing strategy to provide iteration guarantees without prior bounds or iteration counts.

Contribution

It introduces a novel smoothing-based method for convex optimization that handles multiple non-smooth components without requiring prior knowledge of iteration bounds.

Findings

Effective in learning problems like matrix completion and clustering

Provides convergence guarantees independent of iteration count

Handles complex convex objectives with multiple non-smooth parts

Abstract

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.