[Paper Review] Fast-Convergent Dynamics for Distributed Resource Allocation Over Time-Varying Networks.

Mohammadreza Doostmohammadian, Alireza Aghasi+1 more|arXiv (Cornell University)|Dec 15, 2020

Distributed Control Multi-Agent Systems28 references4 citations

TL;DR

This paper proposes a non-Lipschitz distributed dynamics algorithm for resource allocation in time-varying multi-agent networks, where agents optimize local cost functions under a global resource constraint using only local and neighbor information. It achieves fast convergence even over disconnected networks as long as the union of network topologies over bounded intervals contains a spanning tree.

ABSTRACT

In this paper, distributed dynamics are deployed to solve resource allocation over time-varying multi-agent networks. The state of each agent represents the amount of resources used/produced at that agent while the total amount of resources is fixed. The idea is to optimally allocate the resources among the group of agents by reducing the total cost functions subject to fixed amount of total resources. The information of each agent is restricted to its own state and cost function and those of its immediate neighbors. This is motivated by distributed applications such as in mobile edge-computing, economic dispatch over smart grids, and multi-agent coverage control. The non-Lipschitz dynamics proposed in this work shows fast convergence as compared to the linear and some nonlinear solutions in the literature. Further, the multi-agent network connectivity is more relaxed in this paper. To be more specific, the proposed dynamics even reaches optimal solution over time-varying disconnected undirected networks as far as the union of these networks over some bounded non-overlapping time-intervals includes a spanning-tree. The proposed convergence analysis can be applied for similar 1st-order resource allocation nonlinear dynamics. We provide simulations to verify our results.

Motivation & Objective

• To design a distributed resource allocation algorithm that operates efficiently under time-varying network topologies with minimal connectivity assumptions.
• To achieve faster convergence than existing linear and nonlinear distributed dynamics in the literature.
• To enable optimal resource allocation when network connectivity is intermittently disconnected, provided the union of topologies over time intervals contains a spanning tree.
• To develop a convergence analysis applicable to a class of first-order nonlinear dynamics for resource allocation.
• To validate the theoretical results through simulations in realistic distributed settings such as mobile edge computing and smart grids.

Proposed method

• Designs a non-Lipschitz dynamical system where each agent updates its state based on its own cost function and local information from neighbors.
• Implements a consensus-based update rule that ensures all agents converge to a global optimal allocation under fixed total resource constraints.
• Relies on a Lyapunov-based convergence analysis to prove stability and optimality under time-varying network conditions.
• Introduces a condition on the network topology: the union of graphs over non-overlapping time intervals must contain a spanning tree.
• Uses a distributed gradient-like update with a non-smooth, non-Lipschitz term to accelerate convergence compared to linear or standard nonlinear dynamics.
• Applies the analysis to a class of first-order dynamics, enabling broader applicability beyond the specific proposed dynamics.

Experimental results

Research questions

• RQ1 Can distributed resource allocation be achieved with fast convergence in time-varying networks that are not always connected?
• RQ2 How does the proposed non-Lipschitz dynamics compare in convergence speed to linear and standard nonlinear distributed dynamics?
• RQ3 What is the minimal network connectivity requirement for convergence to the optimal solution in time-varying multi-agent systems?
• RQ4 Can the convergence analysis be generalized to other first-order nonlinear dynamics for resource allocation?
• RQ5 Does the proposed method maintain optimality and fast convergence under intermittent network connectivity?

Key findings

• The proposed non-Lipschitz dynamics achieves faster convergence than linear and some nonlinear alternatives in the literature.
• Optimal resource allocation is achieved even when the network is disconnected over time, provided the union of topologies over bounded intervals contains a spanning tree.
• The convergence analysis is generalizable to a class of first-order nonlinear dynamics for distributed resource allocation.
• The method requires only local information—each agent’s own state and cost function, and those of its immediate neighbors—enabling scalable deployment.
• Simulations confirm the theoretical results, demonstrating fast convergence and robustness under time-varying connectivity.