Distributed optimization is a fundamental framework for collaborative inference over networks. The operation is modeled as the joint minimization of a shared objective which typically depends on local observations. Distributed optimization algorithms, such as the distributed alternating direction method of multipliers (D-ADMM), iteratively combine local computations and message exchanges. A main challenge associated with distributed optimization, and particularly with D-ADMM, is that it requires a large number of communications to reach consensus. In this work we proposeunfolded D-ADMM, which follows the emerging deep unfolding methodology to enable D-ADMM to operate reliably with a predefined and small number of messages exchanged by each agent. Unfolded D-ADMM fully preserves the operation of D-ADMM, while leveraging data to tune the hyperparameters of each iteration. These hyperparameters can either be agent-specific, aiming at achieving the best performance within a fixed number of iterations over a given network, or shared among the agents, allowing to learn to distributedly optimize over different networks. We specialize unfolded D-ADMM for two representative settings: a distributed sparse recovery setup, and a distributed machine learning learning scenario. Our numerical results demonstrate that the proposed approach dramatically reduces the number of communications utilized by D-ADMM, without compromising on its performance.

Distributed optimization arises in various applications. A widely-used distributed optimizer is the distributed alternating direction method of multipliers (D-ADMM) algorithm, which enables agents to jointly minimize a shared objective by iteratively combining local computations and message exchanges. However, D-ADMM often involves a large number of possibly costly communications to reach convergence, limiting its applicability in communications-constrained networks. In this work we propose unfolded D-ADMM, which facilitates the application of D-ADMM with limited communications using the emerging deep unfolding methodology. We utilize the conventional D-ADMM algorithm with a fixed number of communications rounds, while leveraging data to tune the hyperparameters of each iteration of the algorithm. By doing so, we learn to optimize with limited communications, while preserving the interpretability and flexibility of the original D-ADMM algorithm. Our numerical results demonstrate that the proposed approach dramatically reduces the number of communications utilized by D-ADMM, without compromising on its performance.