Byzantine-Resilient Decentralized Online Resource Allocation

TL;DR

This paper develops Byzantine-resilient decentralized online resource allocation algorithms that incorporate robust aggregation and clipping techniques, achieving tight regret and constraint violation bounds despite malicious agent behavior.

Contribution

It introduces a novel primal-dual framework with adaptive robust aggregation for Byzantine resilience in decentralized online resource allocation, with theoretical guarantees.

Findings

Algorithms achieve tight linear dynamic regret

Effective mitigation of Byzantine attacks demonstrated

Numerical experiments validate theoretical results

Abstract

In this paper, we investigate the problem of decentralized online resource allocation in the presence of Byzantine attacks. In this problem setting, some agents may be compromised due to external manipulations or internal failures, causing them to behave maliciously and disrupt the resource allocation process by sending incorrect messages to their neighbors. Given the non-consensual nature of the resource allocation problem, we formulate it under a primal-dual optimization framework, where the dual variables are aggregated among the agents, enabling the incorporation of robust aggregation mechanisms to mitigate Byzantine attacks. By leveraging the classical Byzantine attack model, we propose a class of Byzantine-resilient decentralized online resource allocation algorithms that judiciously integrate the adaptive robust clipping technique with the existing robust aggregation rules to filter out adversarial messages. We establish theoretical guarantees, showing that the proposed algorithms achieve tight linear dynamic regret and accumulative constraint violation bounds, where the constants depend on the properties of robust aggregation rules. Numerical experiments on decentralized online economic dispatch validate the effectiveness of our approach and support our theoretical results.