Privacy Distributed Constrained Optimization Over Time-Varying Unbalanced Networks and Its Application in Federated Learning

This paper investigates a class of constrained distributed zeroth-order optimization (ZOO) problems over time-varying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs. We hereby propose a novel algorithm, termed the differential privacy (DP) distributed push-sum based zeroth-order constrained optimization algorithm (DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs, offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm (ZOCOA-FL) to address challenges stemming from the time-varying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares (DLS) and decentralized federated learning (DFL) tasks.