# Fast-Convergent Dynamics for Distributed Allocation of Resources Over Switching Sparse Networks with Quantized Communication Links

arXiv: https://arxiv.org/abs/2012.08181 · HTML: https://mlsanity.com/paper/2012.08181/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [Efficient-Adam: Communication-Efficient Distributed Adam](https://mlsanity.com/paper/2205.14473/) (2022)
- [Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data](https://mlsanity.com/paper/2406.00621/) (2024)
- [Quantization Avoids Saddle Points in Distributed Optimization](https://mlsanity.com/paper/2403.10423/) (2024)
- [Logarithmically Quantized Distributed Optimization over Dynamic Multi-Agent Networks](https://mlsanity.com/paper/2410.20345/) (2024)
- [Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics](https://mlsanity.com/paper/2203.14527/) (2022)
- [D-SVM over Networked Systems with Non-Ideal Linking Conditions](https://mlsanity.com/paper/2304.06667/) (2023)
- [Using Non-Lipschitz Signum-based Functions for Distributed Optimization and Machine Learning: Trade-off Between Con-vergence Rate and Optimality Gap](https://mlsanity.com/paper/2608.01220/) (2026)

## Abstract (arXiv)

This paper proposes networked dynamics to solve resource allocation problems over time-varying multi-agent networks. The state of each agent represents the amount of used resources (or produced utilities) while the total amount of resources is fixed. The idea is to optimally allocate the resources among the group of agents by minimizing the overall cost function subject to fixed sum of resources. Each agents' information is restricted to its own state and cost function and those of its immediate in-neighbors. This is motivated by distributed applications such as mobile edge-computing, economic dispatch over smart grids, and multi-agent coverage control. This work provides a fast convergent solution (in comparison with linear dynamics) while considering relaxed network connectivity with quantized communication links. The proposed dynamics reaches optimal solution over switching (possibly disconnected) undirected networks as far as their union over some bounded non-overlapping time-intervals has a spanning-tree. We prove feasibility of the solution, uniqueness of the optimal state, and convergence to the optimal value under the proposed dynamics, where the analysis is applicable to similar 1st-order allocation dynamics with strongly sign-preserving nonlinearities, such as actuator saturation.