Boosting Verification of Deep Reinforcement Learning via Piece-Wise Linear Decision Neural Networks

Formally verifying deep reinforcement learning (DRL) systems su ff ers from both inaccurate verification results and limited scalability. The major obstacle lies in the large overestimation introduced inherently during training and then transforming the inexplicable decision-making models i.e., deep neural networks (DNNs), into easy-to-verify models. In this paper, we propose an inverse transform-then-train approach, which first encodes a DNN into an equivalent set of e ffi ciently and tightly verifiable linear control policies and then optimizes them via reinforcement learning. We accompany our inverse approach with a novel neural network model called piece-wise linear decision neural networks (PLDNNs), which are compatible with most existing DRL training algorithms with comparable performance against conventional DNNs. Our extensive experiments show that, compared to DNN-based DRL systems, PLDNN-based systems can be more e ffi ciently and tightly verified with up to 438 times speedup and a significant reduction in overestimation. In particular, even a complex 12-dimensional DRL system is e ffi ciently verified with up to 7 times deeper computation steps.