Testing self-healing cyber-physical systems under uncertainty with reinforcement learning: an empirical study

Self-healing is becoming an essential feature of Cyber-Physical Systems (CPSs). CPSs with this feature are named Self-Healing CPSs (SH-CPSs). SH-CPSs detect and recover from errors caused by hardware or software faults at runtime and handle uncertainties arising from their interactions with environments. Therefore, it is critical to test if SH-CPSs can still behave as expected under uncertainties. By testing an SH-CPS in various conditions and learning from testing results, reinforcement learning algorithms can gradually optimize their testing policies and apply the policies to detect failures, i.e., cases that the SH-CPS fails to behave as expected. However, there is insufficient evidence to know which reinforcement learning algorithms perform the best in terms of testing SH-CPSs behaviors including their self-healing behaviors under uncertainties. To this end, we conducted an empirical study to evaluate the performance of 14 combinations of reinforcement learning algorithms, with two value function learning based methods for operation invocations and seven policy optimization based algorithms for introducing uncertainties. Experimental results reveal that the 14 combinations of the algorithms achieved similar coverage of system states and transitions, and the combination of Q-learning and Uncertainty Policy Optimization (UPO) detected the most failures among the 14 combinations. On average, the Q-Learning and UPO combination managed to discover two times more failures than the others. Meanwhile, the combination took 52% less time to find a failure. Regarding scalability, the time and space costs of the value function learning based methods grow, as the number of states and transitions of the system under test increases. In contrast, increasing the system’s complexity has little impact on policy optimization based algorithms.