On the convergence rate of the three operator splitting scheme

TL;DR

This paper provides an alternative proof for the sublinear convergence rate of the three operator splitting scheme, a method for optimizing composite convex functions with smooth and non-smooth terms.

Contribution

It offers a new proof of the convergence rate for the three operator splitting scheme, enhancing theoretical understanding.

Findings

Confirmed sublinear convergence rate

Provided an alternative proof approach

Strengthened theoretical guarantees for the method

Abstract

The three operator splitting scheme was recently proposed by [Davis and Yin, 2015] as a method to optimize composite objective functions with one convex smooth term and two convex (possibly non-smooth) terms for which we have access to their proximity operator. In this short note we provide an alternative proof for the sublinear rate of convergence of this method.