Distributed Gradient-Tracking Optimization with Packet-Error Resilience in Unreliable Networks

In this paper, we address the distributed optimization problem over unreliable error-prone directed networks. We propose a distributed gradient-tracking optimization algorithm (referred to as ARQ-OPT), which exploits packet retransmissions via an Automatic Repeat reQuest (ARQ) error control protocol. Nodes utilize acknowledgement messages transmitted over one-bit error-free channels to trigger retransmissions of packets that were previously received in error. This ensures reliable propagation of information throughout the network, even in the presence of packet errors. We analyze the convergence properties of the proposed algorithm, by augmenting the consensus matrices to align with the retransmission mechanism. Subsequently, we show that by appropriately choosing the maximum number of retransmission attempts, ARQ-OPT can achieve B-step consensus contractivity which allow us to establish asymptotic convergence to the unique optimal solution with probability one. Numerical simulations conducted under various channel conditions validate our findings.