Differentially Private Distributed Online Optimization in Time-varying Networks via Dual Averaging Push

Distributed online optimization allows several nodes in the network to collaboratively minimize the sum of time-varying local cost functions at each moment through information exchange. However, frequent interactions are prone to leakage of sensitive information. Meanwhile, the actual communication networks can be time-varying and unbalanced. To address such a problem, we proposed the differentially private online distributed dual averaging push algorithm (DP-ODDAP), where push-sum protocol and differential privacy are employed on the basis of dual averaging method. By introducing the differential privacy, the data privacy of individuals is protected, which means that malicious nodes gain little sensitive information. Moreover, the impact of the imbalance caused by time-varying directed networks is eliminated by applying push-sum protocol, thus DP-ODDAP can reach the sub-linear expected individual regret bound with order of O(✓T). In addition, the tradeoff between privacy level and accuracy is revealed. Finally, simulation experiments is provided to verify the effectiveness of above results.