Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems
This addresses the challenge of ensuring stability in stochastic control systems, which is crucial for safety-critical applications like robotics or autonomous systems, representing a novel methodological advancement rather than an incremental improvement.
The paper tackles the problem of learning control policies for discrete-time stochastic systems that guarantee probability 1 stability within a specified region, introducing stabilizing ranking supermartingales (sRSMs) to overcome limitations of prior methods and successfully learning provably stabilizing neural network policies in practice.
We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability~$1$. Our approach is based on the novel notion of stabilizing ranking supermartingales (sRSMs) that we introduce in this work. Our sRSMs overcome the limitation of methods proposed in previous works whose applicability is restricted to systems in which the stabilizing region cannot be left once entered under any control policy. We present a learning procedure that learns a control policy together with an sRSM that formally certifies probability~$1$ stability, both learned as neural networks. We show that this procedure can also be adapted to formally verifying that, under a given Lipschitz continuous control policy, the stochastic system stabilizes within some stabilizing region with probability~$1$. Our experimental evaluation shows that our learning procedure can successfully learn provably stabilizing policies in practice.