Bilevel Distributed Optimization in Directed Networks

Understand

Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to cooperatively minimize a global cost function.

• We introduce a new unifying distributed constrained optimization model that is characterized as a bilevel optimization problem.
• This model captures a wide range of existing problems over directed networks including: (i) Distributed optimization with linear constraints; (ii) Distributed unconstrained nonstrongly convex optimization over directed networks.
• Employing a novel regularization-based relaxation approach and gradient-tracking schemes, we develop an iteratively regularized push-pull gradient algorithm.