Private Learning on Networks: Part II
This work addresses privacy in distributed optimization for multi-agent systems, offering incremental improvements through structured randomization.
The paper tackles the problem of distributed multi-agent optimization with privacy concerns by introducing two randomized iterative algorithms that add structured noise to inter-agent communications, ensuring deterministic correctness and proving that a specific algorithm variant preserves privacy for polynomial objective functions under certain network connectivity conditions.
This paper considers a distributed multi-agent optimization problem, with the global objective consisting of the sum of local objective functions of the agents. The agents solve the optimization problem using local computation and communication between adjacent agents in the network. We present two randomized iterative algorithms for distributed optimization. To improve privacy, our algorithms add "structured" randomization to the information exchanged between the agents. We prove deterministic correctness (in every execution) of the proposed algorithms despite the information being perturbed by noise with non-zero mean. We prove that a special case of a proposed algorithm (called function sharing) preserves privacy of individual polynomial objective functions under a suitable connectivity condition on the network topology.