Asynchronous and Stochastic Distributed Resource Allocation

2025-09-01

AI Summary

This paper addresses the asynchronous stochastic resource allocation problem with resource budget constraints in heterogeneous distributed systems, where worker nodes exhibit significant disparities in computational and communication capabilities, high latency, and substantial synchronization overhead. To tackle these challenges, we propose the Asynchronous Stochastic Primal-Dual (Asyn-PD) algorithm. Asyn-PD enables asynchronous node interactions and local stochastic gradient updates without global synchronization, incorporating approximate gradient estimation and a delay-tolerant communication mechanism to mitigate system inconsistency. Theoretically, Asyn-PD is proven to converge to a neighborhood of the original problem’s saddle point at an $O(1/t)$ rate in the second-moment sense. Empirical evaluations demonstrate that Asyn-PD significantly improves convergence speed and resource utilization over synchronous baselines—particularly under high-latency and strongly heterogeneous conditions.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Distributed Machine Learning & Federated Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This work proposes and studies the distributed resource allocation problem in asynchronous and stochastic settings. We consider a distributed system with multiple workers and a coordinating server with heterogeneous computation and communication times. We explore an approximate stochastic primal-dual approach with the aim of 1) adhering to the resource budget constraints, 2) allowing for the asynchronicity between the workers and the server, and 3) relying on the locally available stochastic gradients. We analyze our Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm and prove its convergence in the second moment to the saddle point solution of the approximate problem at the rate of $O(1/t)$, where $t$ is the iteration number. Furthermore, we verify our algorithm numerically to validate the analytically derived convergence results, and demonstrate the advantages of utilizing our asynchronous algorithm rather than deploying a synchronous algorithm where the server must wait until it gets update from all workers.

Problem

• Distributed resource allocation with asynchronous stochastic settings
• Addressing heterogeneous computation and communication times
• Ensuring resource budget constraints with local gradients

Innovation

• Asynchronous stochastic Primal-Dual algorithm
• Distributed resource allocation with heterogeneous times
• Convergence via approximate stochastic primal-dual approach