  We propose a novel data-driven method to accelerate the convergence of
Alternating Direction Method of Multipliers (ADMM) for solving distributed DC
optimal power flow (DC-OPF) where lines are shared between independent network
partitions. Using previous observations of ADMM trajectories for a given system
under varying load, the method trains a recurrent neural network (RNN) to
predict the converged values of dual and consensus variables. Given a new
realization of system load, a small number of initial ADMM iterations is taken
as input to infer the converged values and directly inject them into the
iteration. We empirically demonstrate that the online injection of these values
into the ADMM iteration accelerates convergence by a significant factor for
partitioned 14-, 118- and 2848-bus test systems under differing load scenarios.
The proposed method has several advantages: it maintains the security of
private decision variables inherent in consensus ADMM; inference is fast and so
may be used in online settings; RNN-generated predictions can dramatically
improve time to convergence but, by construction, can never result in
infeasible ADMM subproblems; it can be easily integrated into existing software
implementations. While we focus on the ADMM formulation of distributed DC-OPF
in this paper, the ideas presented are naturally extended to other distributed
optimization problems.
