Towards Parameter-free Distributed Optimization: a Port-Hamiltonian Approach

TL;DR

This paper presents a parameter-free distributed optimization method using port-Hamiltonian systems, enabling stable and fast convergence without the need for parameter tuning, demonstrated through superior numerical performance.

Contribution

It introduces a novel port-Hamiltonian based framework and the MID discretization to achieve parameter-free distributed optimization with guaranteed convergence.

Findings

Outperforms traditional methods in convergence speed

Maintains stability regardless of step size

Effective in scenarios where conventional methods fail

Abstract

This paper introduces a novel distributed optimization technique for networked systems, which removes the dependency on specific parameter choices, notably the learning rate. Traditional parameter selection strategies in distributed optimization often lead to conservative performance, characterized by slow convergence or even divergence if parameters are not properly chosen. In this work, we propose a systems theory tool based on the port-Hamiltonian formalism to design algorithms for consensus optimization programs. Moreover, we propose the Mixed Implicit Discretization (MID), which transforms the continuous-time port-Hamiltonian system into a discrete time one, maintaining the same convergence properties regardless of the step size parameter. The consensus optimization algorithm enhances the convergence speed without worrying about the relationship between parameters and stability. Numerical experiments demonstrate the method's superior performance in convergence speed, outperforming other methods, especially in scenarios where conventional methods fail due to step size parameter limitations.