Automated Performance Estimation for Decentralized Optimization via Network Size Independent Problems

by   Sebastien Colla, et al.

We develop a novel formulation of the Performance Estimation Problem (PEP) for decentralized optimization whose size is independent of the number of agents in the network. The PEP approach allows computing automatically the worst-case performance and worst-case instance of first-order optimization methods by solving an SDP. Unlike previous work, the size of our new PEP formulation is independent of the network size. For this purpose, we take a global view of the decentralized problem and we also decouple the consensus subspace and its orthogonal complement. We apply our methodology to different decentralized methods such as DGD, DIGing and EXTRA and obtain numerically tight performance guarantees that are valid for any network size.


page 1

page 2

page 3

page 4


Automatic Performance Estimation for Decentralized Optimization

We present a methodology to automatically compute worst-case performance...

Automated Worst-Case Performance Analysis of Decentralized Gradient Descent

We develop a methodology to automatically compute worst-case performance...

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

PEPit is a Python package aiming at simplifying the access to worst-case...

Optimization-based Decentralized Coded Caching for Files and Caches with Arbitrary Size

Existing decentralized coded caching solutions cannot guarantee small lo...

Decentralized Control of Cooperative Systems: Categorization and Complexity Analysis

Decentralized control of cooperative systems captures the operation of a...

Quantization for decentralized learning under subspace constraints

In this paper, we consider decentralized optimization problems where age...

CHERI Performance Enhancement for a Bytecode Interpreter

During our port of the MicroPython bytecode interpreter to the CHERI-bas...

Please sign up or login with your details

Forgot password? Click here to reset