Counter-example Guided Learning of Bounds on Environment Behavior

There is a growing interest in building autonomous systems that interact with complex environments. The difficulty associated with obtaining an accurate model for such environments poses a challenge to the task of assessing and guaranteeing the system's performance. We present a data-driven solution that allows for a system to be evaluated for specification conformance without an accurate model of the environment. Our approach involves learning a conservative reactive bound of the environment's behavior using data and specification of the system's desired behavior. First, the approach begins by learning a conservative reactive bound on the environment's actions that captures its possible behaviors with high probability. This bound is then used to assist verification, and if the verification fails under this bound, the algorithm returns counter-examples to show how failure occurs and then uses these to refine the bound. We demonstrate the applicability of the approach through two case-studies: i) verifying controllers for a toy multi-robot system, and ii) verifying an instance of human-robot interaction during a lane-change maneuver given real-world human driving data

A Note on High-Probability versus In-Expectation Guarantees of Generalization Bounds in Machine Learning

Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample that is not representative of the underlying distribution, one cannot expect to construct a reliable machine learning model. Following that, statements made about the performance of machine learning models have to take the sampling process into account. The two common approaches for that are to generate statements that hold either in high-probability, or in-expectation, over the random sampling process. In this short note we show how one may transform one statement to another. As a technical novelty we address the case of unbounded loss function, where we use a fairly new assumption, called the witness condition

Stability and Deviation Optimal Risk Bounds with Convergence Rate O(1/n)O(1/n)

The sharpest known high probability generalization bounds for uniformly stable algorithms (Feldman, Vondr\'{a}k, 2018, 2019), (Bousquet, Klochkov, Zhivotovskiy, 2020) contain a generally inevitable sampling error term of order $\Theta(1/\sqrt{n})$. When applied to excess risk bounds, this leads to suboptimal results in several standard stochastic convex optimization problems. We show that if the so-called Bernstein condition is satisfied, the term $\Theta(1/\sqrt{n})$ can be avoided, and high probability excess risk bounds of order up to $O(1/n)$ are possible via uniform stability. Using this result, we show a high probability excess risk bound with the rate $O(\log n/n)$ for strongly convex and Lipschitz losses valid for \emph{any} empirical risk minimization method. This resolves a question of Shalev-Shwartz, Shamir, Srebro, and Sridharan (2009). We discuss how $O(\log n/n)$ high probability excess risk bounds are possible for projected gradient descent in the case of strongly convex and Lipschitz losses without the usual smoothness assumption.Comment: 12 pages; presented at NeurIP

Scalable Synthesis and Verification: Towards Reliable Autonomy

We have seen the growing deployment of autonomous systems in our daily life, ranging from safety-critical self-driving cars to dialogue agents. While impactful and impressive, these systems do not often come with guarantees and are not rigorously evaluated for failure cases. This is in part due to the limited scalability of tools available for designing correct-by-construction systems, or verifying them posthoc. Another key limitation is the lack of availability of models for the complex environments with which autonomous systems often have to interact with. In the direction of overcoming these above mentioned bottlenecks to designing reliable autonomous systems, this thesis makes contributions along three fronts. First, we develop an approach for parallelized synthesis from linear-time temporal logic Specifications corresponding to the generalized reactivity (1) fragment. We begin by identifying a special case corresponding to singleton liveness goals that allows for a decomposition of the synthesis problem, which facilitates parallelized synthesis. Based on the intuition from this special case, we propose a more generalized approach for parallelized synthesis that relies on identifying equicontrollable states. Second, we consider learning-based approaches to enable verification at scale for complex systems, and for autonomous systems that interact with black-box environments. For the former, we propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. For the latter, we present a data-driven approach based on chance-constrained optimization that allows for a system to be evaluated for specification conformance without an accurate model of the environment. We demonstrate this approach on several tasks, including a lane-change scenario with real-world driving data. Lastly, we consider the problem of interpreting and verifying learning-based components such as neural networks. We introduce a new method based on Craig's interpolants for computing compact symbolic abstractions of pre-images for neural networks. Our approach relies on iteratively computing approximations that provably overapproximate and underapproximate the pre-images at all layers. Further, building on existing work for training neural networks for verifiability in the classification setting, we propose extensions that allow us to generalize the approach to more general architectures and temporal specifications.</p