Distributed Optimization of Convex Sum of Non-Convex Functions
This work addresses distributed optimization challenges for networks of agents with private non-convex data, but it is incremental as it builds on an existing algorithm with an added assumption.
The paper tackles the problem of distributed optimization of a convex sum of non-convex functions, where each function is privately held by an agent in a network, and shows that a coupled consensus and projected gradient descent algorithm can optimize this under an additional gradient Lipschitzness assumption, with applications to improving privacy in distributed optimization.
We present a distributed solution to optimizing a convex function composed of several non-convex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show that coupled consensus and projected gradient descent algorithm proposed in [1] can optimize convex sum of non-convex functions under an additional assumption on gradient Lipschitzness. We further discuss the applications of this analysis in improving privacy in distributed optimization.