We study the problem of learning controllers for discrete-time non-linear
stochastic dynamical systems with formal reach-avoid guarantees. This work
presents the first method for providing formal reach-avoid guarantees, which
combine and generalize stability and safety guarantees, with a tolerable
probability threshold $p\in[0,1]$ over the infinite time horizon. Our method
leverages advances in machine learning literature and it represents formal
certificates as neural networks. In particular, we learn a certificate in the
form of a reach-avoid supermartingale (RASM), a novel notion that we introduce
in this work. Our RASMs provide reachability and avoidance guarantees by
imposing constraints on what can be viewed as a stochastic extension of level
sets of Lyapunov functions for deterministic systems. Our approach solves
several important problems -- it can be used to learn a control policy from
scratch, to verify a reach-avoid specification for a fixed control policy, or
to fine-tune a pre-trained policy if it does not satisfy the reach-avoid
specification. We validate our approach on $3$ stochastic non-linear
reinforcement learning tasks.

本论文介绍了一种利用神经网络提供形式化到达 - 避免保证的方法，通过在随机非线性动态系统中学习控制器来解决实现证明的问题，以及提出了超级马丁格尔的概念作为证明，并通过对 Lyapunov 函数的确定性系统的随机扩展上的级集的约束来提供可达性和避开保证。