Differentially Private Dual Gradient Tracking for Distributed Resource Allocation
CoRR(2024)
Abstract
This paper investigates privacy issues in distributed resource allocation
over directed networks, where each agent holds a private cost function and
optimizes its decision subject to a global coupling constraint through local
interaction with other agents. Conventional methods for resource allocation
over directed networks require all agents to transmit their original data to
neighbors, which poses the risk of disclosing sensitive and private
information. To address this issue, we propose an algorithm called
differentially private dual gradient tracking (DP-DGT) for distributed resource
allocation, which obfuscates the exchanged messages using independent Laplacian
noise. Our algorithm ensures that the agents' decisions converge to a
neighborhood of the optimal solution almost surely. Furthermore, without the
assumption of bounded gradients, we prove that the cumulative differential
privacy loss under the proposed algorithm is finite even when the number of
iterations goes to infinity. To the best of our knowledge, we are the first to
simultaneously achieve these two goals in distributed resource allocation
problems over directed networks. Finally, numerical simulations on economic
dispatch problems within the IEEE 14-bus system illustrate the effectiveness of
our proposed algorithm.
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