Constrained Feedforward Neural Network Training via Reachability Analysis
This addresses safety-critical applications like robotics near humans, but it is incremental as it builds on existing verification methods.
The paper tackles the challenge of training neural networks to obey safety constraints by proposing a constrained training method that simultaneously trains and verifies feedforward ReLU networks using reachability analysis, demonstrated on a small network with one nonlinearity layer and about 50 parameters.
Neural networks have recently become popular for a wide variety of uses, but have seen limited application in safety-critical domains such as robotics near and around humans. This is because it remains an open challenge to train a neural network to obey safety constraints. Most existing safety-related methods only seek to verify that already-trained networks obey constraints, requiring alternating training and verification. Instead, this work proposes a constrained method to simultaneously train and verify a feedforward neural network with rectified linear unit (ReLU) nonlinearities. Constraints are enforced by computing the network's output-space reachable set and ensuring that it does not intersect with unsafe sets; training is achieved by formulating a novel collision-check loss function between the reachable set and unsafe portions of the output space. The reachable and unsafe sets are represented by constrained zonotopes, a convex polytope representation that enables differentiable collision checking. The proposed method is demonstrated successfully on a network with one nonlinearity layer and approximately 50 parameters.