GLinSAT: The General Linear Satisfiability Neural Network Layer By Accelerated Gradient Descent

Ensuring that the outputs of neural networks satisfy specific constraints is crucial for applying neural networks to real-life decision-making problems. In this paper, we consider making a batch of neural network outputs satisfy bounded and general linear constraints. We first reformulate the neural network output projection problem as an entropy-regularized linear programming problem. We show that such a problem can be equivalently transformed into an unconstrained convex optimization problem with Lipschitz continuous gradient according to the duality theorem. Then, based on an accelerated gradient descent algorithm with numerical performance enhancement, we present our architecture, GLinSAT, to solve the problem. To the best of our knowledge, this is the first general linear satisfiability layer in which all the operations are differentiable and matrix-factorization-free. Despite the fact that we can explicitly perform backpropagation based on automatic differentiation mechanism, we also provide an alternative approach in GLinSAT to calculate the derivatives based on implicit differentiation of the optimality condition. Experimental results on constrained traveling salesman problems, partial graph matching with outliers, predictive portfolio allocation and power system unit commitment demonstrate the advantages of GLinSAT over existing satisfiability layers.

Transmission Interface Power Flow Adjustment: A Deep Reinforcement Learning Approach based on Multi-task Attribution Map

Transmission interface power flow adjustment is a critical measure to ensure the security and economy operation of power systems. However, conventional model-based adjustment schemes are limited by the increasing variations and uncertainties occur in power systems, where the adjustment problems of different transmission interfaces are often treated as several independent tasks, ignoring their coupling relationship and even leading to conflict decisions. In this paper, we introduce a novel data-driven deep reinforcement learning (DRL) approach, to handle multiple power flow adjustment tasks jointly instead of learning each task from scratch. At the heart of the proposed method is a multi-task attribution map (MAM), which enables the DRL agent to explicitly attribute each transmission interface task to different power system nodes with task-adaptive attention weights. Based on this MAM, the agent can further provide effective strategies to solve the multi-task adjustment problem with a near-optimal operation cost. Simulation results on the IEEE 118-bus system, a realistic 300-bus system in China, and a very large European system with 9241 buses demonstrate that the proposed method significantly improves the performance compared with several baseline methods, and exhibits high interpretability with the learnable MAM.