到達可能性解析による制約付きフィードフォワードニューラルネットワークの学習
Constrained Feedforward Neural Network Training via Reachability Analysis
ReLUネットワークの出力空間の到達可能集合を制約ゾノトープで計算し、不安全集合との衝突を防ぐ損失関数で学習と検証を同時に行う手法を提案した。
著者: Long Kiu Chung, Adam Dai, Derek Knowles, Shreyas Kousik, Grace X. Gao
分類: cs.LG, cs.AI, cs.RO
原文アブストラクト
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.
