Główne pojęcia
The proposed distributed accelerated gradient flow algorithm achieves a convergence rate of O(1/t^(2-β)) for smooth convex optimization problems, which is near-optimal in the distributed setting.
Streszczenie
The key highlights and insights from the content are:
The paper introduces a distributed continuous-time gradient flow method, called Dist-AGM, that aims to minimize the sum of smooth convex functions. Dist-AGM achieves an unprecedented convergence rate of O(1/t^(2-β)), where β > 0 can be arbitrarily small.
The authors establish an energy conservation perspective on optimization algorithms, where the associated energy functional remains conserved within a dilated coordinate system. This generalized framework can be used to analyze the convergence rates of a wide range of distributed optimization algorithms.
The authors provide a consistent rate-matching discretization of Dist-AGM using the Symplectic Euler method, ensuring that the discretized algorithm achieves a convergence rate of O(1/k^(2-β)), where k represents the number of iterations.
Experimental results demonstrate the accelerated convergence behavior of the proposed distributed optimization algorithm, particularly on problems with poor condition numbers.
Statystyki
The key metrics and figures used to support the authors' claims are:
The proposed Dist-AGM algorithm achieves a convergence rate of O(1/t^(2-β)), where β > 0 can be arbitrarily small.
The discretized version of Dist-AGM achieves a convergence rate of O(1/k^(2-β)), where k represents the number of iterations.