  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.
