PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python

TL;DR

PEPit is a Python package that automates worst-case performance analysis of various first-order optimization algorithms by translating the problem into a solvable semidefinite program, simplifying the analysis process.

Contribution

The paper introduces PEPit, a Python tool that streamlines worst-case analysis of first-order methods through automatic SDP formulation and solution, enhancing accessibility and efficiency.

Findings

Enables computer-assisted worst-case analysis of diverse first-order methods.

Simplifies the process by allowing users to implement methods as usual.

Provides numerical worst-case bounds via SDP solvers.

Abstract

PEPit is a Python package aiming at simplifying the access to worst-case analyses of a large family of first-order optimization methods possibly involving gradient, projection, proximal, or linear optimization oracles, along with their approximate, or Bregman variants. In short, PEPit is a package enabling computer-assisted worst-case analyses of first-order optimization methods. The key underlying idea is to cast the problem of performing a worst-case analysis, often referred to as a performance estimation problem (PEP), as a semidefinite program (SDP) which can be solved numerically. To do that, the package users are only required to write first-order methods nearly as they would have implemented them. The package then takes care of the SDP modeling parts, and the worst-case analysis is performed numerically via a standard solver.