SD-PPDDA: A Privacy Efficient Decentralized Dual Averaging Algorithm Over Networks

Abstract

This paper studies a decentralized online constrained optimization problem characterized by a shared constraint set. Nodes in the communication and learning network conduct local computations and communications to collaboratively solve the problem. Each node can access its own local cost function, whose value depends on its decision at each time step. However, because nodes continuously exchange privacy-sensitive information, most existing algorithms for this problem are susceptible to privacy leakage. To address this challenge, we propose an effective state-decomposition-based privacy-preserving decentralized dual averaging (SD-PPDDA) algorithm. The SD-PPDDA algorithm employs state decomposition scheme to preserve privacy without introducing additional hidden signals (may cause additional optimization errors) or incurring significant computational overhead. Theoretical analysis shows that the SD-PPDDA algorithm achieves the desired sublinear regret, specifically converging at a rate of $\mathcal {O} \left ({{ \sqrt {K} }}\right) $ (where $K$ denotes the number of iterations), while preserving the privacy of each node’s cost function. In addition, numerical simulations further validate the convergence and practicality of the algorithm.