The desire to use reinforcement learning in safety-critical settings has inspired a recent interest in formal methods for learning algorithms. Existing formal methods for learning and optimization primarily consider the problem of constrained learning or constrained optimization. Given a single correct model and associated safety constraint, these approaches guarantee efficient learning while provably avoiding behaviors outside the safety constraint. Acting well given an accurate environmental model is an important pre-requisite for safe learning, but is ultimately insufficient for systems that operate in complex heterogeneous environments. This paper introduces verification-preserving model updates, the first approach toward obtaining formal safety guarantees for reinforcement learning in settings where multiple possible environmental models must be taken into account. Through a combination of inductive data and deductive proving with design-time model updates and runtime model falsification, we provide a first approach toward obtaining formal safety proofs for autonomous systems acting in heterogeneous environments.
Although we are the first to explore hybrid program repair, several researchers have explored the problem of synthesizing hybrid systems from data @cite_19 @cite_9 . This work is closely related to our update. Sadraddini and Belta provide formal guarantees for data-driven model identification and controller synthesis @cite_9 . Relative to this work, our update is continuous-time, synthesizes a computer-checked correctness proof (as opposed to a least violation criterion implied by the synthesis algorithm, both not independently checked by a theorem prover), and does not require dynamics to be compact, bounded, and locally connected. Unlike @cite_19 , our full set of model updates is sometimes capable of synthesizing nonlinear dynamical systems from data (e.g., the static @math circular update) and produces computer-checked correctness proofs for permissive controllers.
@cite_19 @cite_9
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Controller synthesis for hybrid systems that satisfy temporal specifications expressing various system properties is a challenging problem that has drawn the attention of many researchers. However, making the assumption that such temporal properties are deterministic is far from the reality. For example, many of the properties the controller has to satisfy are learned through machine learning techniques based on sensor input data. In this paper, we propose a new logic, Probabilistic Signal Temporal Logic (PrSTL), as an expressive language to define the stochastic properties, and enforce probabilistic guarantees on them. We further show how to synthesize safe controllers using this logic for cyber-physical systems under the assumption that the stochastic properties are based on a set of Gaussian random variables. One of the key distinguishing features of PrSTL is that the encoded logic is adaptive and changes as the system encounters additional data and updates its beliefs about the latent random variables that define the safety properties. We demonstrate our approach by synthesizing safe controllers under the PrSTL specifications for multiple case studies including control of quadrotors and autonomous vehicles in dynamic environments. This paper presents a bounded model checking tool called @math for hybrid systems. It translates a reachability problem of a nonlinear hybrid system into a predicate logic formula involving arithmetic constraints and checks the satisfiability of the formula based on a satisfiability modulo theories method. We tightly integrate (i) an incremental SAT solver to enumerate the possible sets of constraints and (ii) an interval-based solver for hybrid constraint systems (HCSs) to solve the constraints described in the formulas. The HCS solver verifies the occurrence of a discrete change by using a set of boxes to enclose continuous states that may cause the discrete change. We utilize the existence property of a unique solution in the boxes computed by the HCS solver as (i) a proof of the reachability of a model and (ii) a guide in the over-approximation refinement procedure. Our @math implementation successfully handled several examples including those with nonlinear constraints. We present a novel and scalable policy synthesis approach for robots. Rather than producing single-path plans for a static environment, we consider changing environments with uncontrollable agents, where the robot needs a policy to respond correctly over the infinite-horizon interaction with the environment. Our approach operates on task and motion domains, and combines actions over discrete states with continuous, collision-free paths. We synthesize a task and motion policy by iteratively generating a candidate policy and verifying its correctness. For efficient policy generation, we use grammars for potential policies to limit the search space and apply domain-specific heuristics to generalize verification failures, providing stricter constraints on policy candidates. For efficient policy verification, we construct compact, symbolic constraints for valid policies and employ a Satisfiability Modulo Theories (SMT) solver to check the validity of these constraints. Furthermore, the SMT solver enables quantitative specifications such as energy limits. The results show that our approach offers better scalability compared to a state-of-the-art policy synthesis tool in the tested benchmarks and demonstrate an order-of-magnitude speedup from our heuristics for the tested mobile manipulation domain. This paper considers Bayesian data fusion of conventional robot sensor information with ambiguous human-generated categorical information about continuous world states of interest. First, it is shown that such soft information can be generally modeled via hybrid continuous-to-discrete likelihoods that are based on the softmax function. A new hybrid fusion procedure, called variational Bayesian importance sampling (VBIS), is then introduced to combine the strengths of variational Bayes approximations and fast Monte Carlo methods to produce reliable posterior estimates for Gaussian priors and softmax likelihoods. VBIS is then extended to more general fusion problems that involve complex Gaussian mixture (GM) priors and multimodal softmax likelihoods, leading to accurate GM approximations of highly non-Gaussian fusion posteriors for a wide range of robot sensor data and soft human data. Experiments for hardware-based multitarget search missions with a cooperative human-autonomous robot team show that humans can serve as highly informative sensors through proper data modeling and fusion, and that VBIS provides reliable and scalable Bayesian fusion estimates via GMs.