TY - GEN AB - In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of how to learn such policies is little explored. Here, we study the effectiveness of jointly learning a policy together with a martingale certificate that proves its stability using a single learning algorithm. We observe that the joint optimization problem becomes easily stuck in local minima when starting from a randomly initialized policy. Our results suggest that some form of pre-training of the policy is required for the joint optimization to repair and verify the policy successfully. AU - Zikelic, Dorde AU - Lechner, Mathias AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A ID - 14601 T2 - arXiv TI - Learning stabilizing policies in stochastic control systems ER - TY - GEN AB - 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. AU - Zikelic, Dorde AU - Lechner, Mathias AU - Henzinger, Thomas A AU - Chatterjee, Krishnendu ID - 14600 T2 - arXiv TI - Learning control policies for stochastic systems with reach-avoid guarantees ER - TY - JOUR AB - Gradual typing is a principled means for mixing typed and untyped code. But typed and untyped code often exhibit different programming patterns. There is already substantial research investigating gradually giving types to code exhibiting typical untyped patterns, and some research investigating gradually removing types from code exhibiting typical typed patterns. This paper investigates how to extend these established gradual-typing concepts to give formal guarantees not only about how to change types as code evolves but also about how to change such programming patterns as well. In particular, we explore mixing untyped "structural" code with typed "nominal" code in an object-oriented language. But whereas previous work only allowed "nominal" objects to be treated as "structural" objects, we also allow "structural" objects to dynamically acquire certain nominal types, namely interfaces. We present a calculus that supports such "cross-paradigm" code migration and interoperation in a manner satisfying both the static and dynamic gradual guarantees, and demonstrate that the calculus can be implemented efficiently. AU - Mühlböck, Fabian AU - Tate, Ross ID - 10153 JF - Proceedings of the ACM on Programming Languages KW - gradual typing KW - gradual guarantee KW - nominal KW - structural KW - call tags TI - Transitioning from structural to nominal code with efficient gradual typing VL - 5 ER - TY - CONF AB - We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR. AU - Grunbacher, Sophie AU - Hasani, Ramin AU - Lechner, Mathias AU - Cyranka, Jacek AU - Smolka, Scott A AU - Grosu, Radu ID - 10669 IS - 13 SN - 2159-5399 T2 - Proceedings of the AAAI Conference on Artificial Intelligence TI - On the verification of neural ODEs with stochastic guarantees VL - 35 ER - TY - CONF AB - We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system’s dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the trajectory length measure in a latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. AU - Hasani, Ramin AU - Lechner, Mathias AU - Amini, Alexander AU - Rus, Daniela AU - Grosu, Radu ID - 10671 IS - 9 SN - 2159-5399 T2 - Proceedings of the AAAI Conference on Artificial Intelligence TI - Liquid time-constant networks VL - 35 ER -