  Many decision-making problems in engineering applications such as
transportation, power system and operations research require repeatedly solving
large-scale linear programming problems with a large number of different
inputs. For example, in energy systems with high levels of uncertain renewable
resources, tens of thousands of scenarios may need to be solved every few
minutes. Standard iterative algorithms for linear network flow problems, even
though highly efficient, becomes a bottleneck in these applications. In this
work, we propose a novel learning approach to accelerate the solving process.
By leveraging the rich theory and economic interpretations of LP duality, we
interpret the output of the neural network as a noisy codeword, where the
codebook is given by the optimization problem's KKT conditions. We propose a
feedforward decoding strategy that finds the optimal set of active constraints.
This design is error correcting and can offer orders of magnitude speedup
compared to current state-of-the-art iterative solvers, while providing much
better solutions in terms of feasibility and optimality compared to end-to-end
learning approaches.
