Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.Comment: 8 pages, 9 figures, to appear in TNNL

THE PRICE OF NON-COOPERATION IN RESERVATION-BASED BANDWIDTH SHARING PROTOCOLS

ABSTRACTIn reservation-based bandwidth sharing protocols, the base station relies on the stations’ requests to allocate time slots to them. Like most  other protocols, reservation-based protocols were designed with the assumption that all stationsrespect the rules of the protocols. However, as mobile devices are becoming more intelligent andprogrammable, they can selfishly optimize their operations to obtain a larger share of commonbandwidth. Here, we study reservation-based bandwidth sharing protocols considering the existence of selfish stations through game-theoretic perspectives. We show that this game admits a Nash  equilibrium. Then, we prove the inefficiency of the Nash equilibrium. Game-theoretical analysis shows that local optimization in the bandwidth sharing problem with conflicted interests does not lead to any global optimization.Keywords. Nash equilibrium, Repeated game, Reservation-based