Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Accelerated Distributed Allocation

Mohammadreza Doostmohammadian, Alireza Aghasi

TL;DR

This paper addresses fast, distributed resource allocation with a fixed total budget by introducing a signum-based, rate-tunable continuous-time (and discrete-time) dynamics over uniformly-connected networks that preserves feasibility at all times. The method achieves convergence to the unique optimum where the gradient of the aggregate cost lies in the span of the all-ones vector, without requiring all-time connectivity. Key contributions include relaxing all-time connectivity, establishing all-time feasibility, and providing a tunable acceleration via $0<\alpha<1$ and $\beta>1$, demonstrated with simulations that outperform several primal-based baselines. The approach is practical for large-scale, dynamic networks and offers robustness considerations for future work in noisy, lossy, or adversarial settings.

Abstract

Distributed allocation finds applications in many scenarios including CPU scheduling, distributed energy resource management, and networked coverage control. In this paper, we propose a fast convergent optimization algorithm with a tunable rate using the signum function. The convergence rate of the proposed algorithm can be managed by changing two parameters. We prove convergence over uniformly-connected multi-agent networks. Therefore, the solution converges even if the network loses connectivity at some finite time intervals. The proposed algorithm is all-time feasible, implying that at any termination time of the algorithm, the resource-demand feasibility holds. This is in contrast to asymptotic feasibility in many dual formulation solutions (e.g., ADMM) that meet resource-demand feasibility over time and asymptotically.

Accelerated Distributed Allocation

TL;DR

This paper addresses fast, distributed resource allocation with a fixed total budget by introducing a signum-based, rate-tunable continuous-time (and discrete-time) dynamics over uniformly-connected networks that preserves feasibility at all times. The method achieves convergence to the unique optimum where the gradient of the aggregate cost lies in the span of the all-ones vector, without requiring all-time connectivity. Key contributions include relaxing all-time connectivity, establishing all-time feasibility, and providing a tunable acceleration via and , demonstrated with simulations that outperform several primal-based baselines. The approach is practical for large-scale, dynamic networks and offers robustness considerations for future work in noisy, lossy, or adversarial settings.

Abstract

Distributed allocation finds applications in many scenarios including CPU scheduling, distributed energy resource management, and networked coverage control. In this paper, we propose a fast convergent optimization algorithm with a tunable rate using the signum function. The convergence rate of the proposed algorithm can be managed by changing two parameters. We prove convergence over uniformly-connected multi-agent networks. Therefore, the solution converges even if the network loses connectivity at some finite time intervals. The proposed algorithm is all-time feasible, implying that at any termination time of the algorithm, the resource-demand feasibility holds. This is in contrast to asymptotic feasibility in many dual formulation solutions (e.g., ADMM) that meet resource-demand feasibility over time and asymptotically.
Paper Structure (5 sections, 5 theorems, 12 equations, 2 figures, 1 algorithm)

This paper contains 5 sections, 5 theorems, 12 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. The Proposed Accelerated Algorithm
  4. Simulations
  5. Conclusions

Key Result

Lemma 1

boyd2006optimal The strictly convex constrained optimization problem eq_dra has a unique optimal solution ${\mathbf{x}^*}$ for which the objective gradient satisfies $\nabla F({\mathbf{x}^*}) \in \hbox{span}(\mathbf{1}_n)$, where $\nabla F({\mathbf{x}^*}) := (\frac{df_1}{dx_1}(x_1^*),\dots,\frac{df_

Figures (2)

  • Figure 1: (Left) Time-evolution of the residual value under the proposed accelerated dynamics \ref{['eq_solution0']} as compared with some existing literature: linear cherukuri2015distributed, accelerated linear with $b=0.5$shames2011accelerated, finite-time with $\nu=0.7$chen2016distributed, and saturated with $\delta =1$cctascl solutions (Right) Time-evolution of the state values of all agents under the proposed dynamics.
  • Figure 2: (Left) The residual decay rate for different $\alpha$ and $\beta$ values under dynamics \ref{['eq_solution0']}. (Right) The residual evolution under discrete-time dynamics \ref{['eq_sol_d']} for different $\alpha$, $\beta$, and $\eta$ values.

Theorems & Definitions (11)

  • Lemma 1
  • proof
  • Remark 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 1
  • ...and 1 more