  One potential future for the next generation of smart grids is the use of
decentralized optimization algorithms and secured communications for
coordinating renewable generation (e.g., wind/solar), dispatchable devices
(e.g., coal/gas/nuclear generations), demand response, battery & storage
facilities, and topology optimization. The Alternating Direction Method of
Multipliers (ADMM) has been widely used in the community to address such
decentralized optimization problems and, in particular, the AC Optimal Power
Flow (AC-OPF). This paper studies how machine learning may help in speeding up
the convergence of ADMM for solving AC-OPF. It proposes a novel decentralized
machine-learning approach, namely ML-ADMM, where each agent uses deep learning
to learn the consensus parameters on the coupling branches. The paper also
explores the idea of learning only from ADMM runs that exhibit high-quality
convergence properties, and proposes filtering mechanisms to select these runs.
Experimental results on test cases based on the French system demonstrate the
potential of the approach in speeding up the convergence of ADMM significantly.
