Federated optimization, wherein several agents in a network collaborate with a central server to achieve optimal social cost over the network with no requirement for exchanging information among agents, has attracted significant interest from the research community. In this context, agents demand resources based on their local computation. Due to the exchange of optimization parameters such as states, constraints, or objective functions with a central server, an adversary may infer sensitive information of agents. We develop a differentially-private additive-increase and multiplicative-decrease algorithm to allocate multiple divisible shared heterogeneous resources to agents in a network. The developed algorithm provides a differential privacy guarantee to each agent in the network. The algorithm does not require inter-agent communication, and the agents do not need to share their cost function or their derivatives with other agents or a central server; however, they share their allocation states with a central server that keeps track of the aggregate consumption of resources. The algorithm incurs very little communication overhead; for m heterogeneous resources in the system, the asymptotic upper bound on the communication complexity is O(m) bits at a time step. Furthermore, if the algorithm converges in K time steps, then the upper bound communication complexity will be O(mK) bits. The algorithm can find applications in several areas, including smart cities, smart energy systems, resource management in the sixth generation (6G) wireless networks with privacy guarantees, etc. We present experimental results to check the efficacy of the algorithm. Furthermore, we present empirical analyses for the trade-off between privacy and algorithm efficiency.

翻译：联邦优化作为一种使网络中多个智能体在与中央服务器协作下实现全局最优社交成本而无需智能体间信息交换的方法，已引起研究界的广泛兴趣。在此框架下，智能体依据本地计算需求资源。由于需向中央服务器传输状态、约束或目标函数等优化参数，攻击者可能推断出智能体的敏感信息。为此，我们提出一种基于差分隐私的加法递增乘法递减算法，用于向网络中智能体分配多种可分异构共享资源。该算法为网络中每个智能体提供差分隐私保护，无需智能体间通信，且智能体无需与其它智能体或中央服务器共享其成本函数或导数；但需将分配状态发送至中央服务器，由后者追踪资源总消耗量。该算法通信开销极低：对于系统中m种异构资源，单步通信复杂度的渐近上界为O(m)比特。若算法在K步内收敛，则总通信复杂度上界为O(mK)比特。本算法可应用于智慧城市、智能能源系统、第六代（6G）无线网络资源管理（需隐私保障）等多个领域。我们通过实验结果验证算法有效性，并基于实证分析探讨隐私保护与算法效率间的权衡关系。