Distributed Learn-to-Optimize: Limited Communications Optimization Over Networks via Deep Unfolded Distributed ADMM

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 propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unfolded D-ADMM</i>, 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.