Robustness and Convergence Analysis of First-Order Distributed Optimization Algorithms over Subspace Constraints

TL;DR

This paper analyzes the robustness and convergence of extended decentralized gradient descent algorithms over subspace constraints using the integral quadratic constraint framework, demonstrating their effectiveness in multitask inference.

Contribution

It introduces a generalized analysis framework for distributed optimization algorithms over subspace constraints, extending prior algorithms to broader problem settings.

Findings

Framework effectively assesses worst-case robustness and convergence.

Extended algorithms successfully solve multitask inference problems.

Demonstrates applicability of the analysis to practical distributed optimization scenarios.

Abstract

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint framework, we analyze the performance of these generalized algorithms in terms of worst-case robustness and convergence rate. The utility of our framework is demonstrated by showing how one of the extended algorithms, originally designed for consensus, is now able to solve a multitask inference problem.