Event-triggered Dual Gradient Tracking for Distributed Resource Allocation

TL;DR

This paper presents an event-triggered dual gradient tracking algorithm for distributed resource allocation that reduces communication overhead while maintaining convergence guarantees, suitable for resource-constrained networks.

Contribution

It introduces a novel event-triggered communication scheme for dual gradient tracking, providing convergence analysis under various conditions, and demonstrating reduced communication with maintained performance.

Findings

Significantly reduces communication events compared to periodic schemes.

Achieves sublinear convergence for non-convex dual objectives.

Attains linear convergence under Polyak-Łojasiewicz condition.

Abstract

High communication costs create a major bottleneck for distributed resource allocation over unbalanced directed networks. Conventional dual gradient tracking methods, while effective for problems on unbalanced digraphs, rely on periodic communication that creates significant overhead in resource-constrained networks. This paper introduces a novel event-triggered dual gradient tracking algorithm to mitigate this limitation, wherein agents communicate only when local state deviations surpass a predefined threshold. We establish comprehensive convergence guarantees for this approach. First, we prove sublinear convergence for non-convex dual objectives and linear convergence under the Polyak-{\L}ojasiewicz condition. Building on this, we demonstrate that the proposed algorithm achieves sublinear convergence for general strongly convex cost functions and linear convergence for those that are also Lipschitz-smooth. Numerical experiments confirm that our event-triggered method significantly reduces communication events compared to periodic schemes while preserving comparable convergence performance.