publications

* indicates equal contribution

preprints

2026

1. 

   Probably Approximately Correct (PAC) Guarantees for Data-Driven Reachability Analysis: A Theoretical and Empirical Comparison

   Elizabeth Dietrich^*, Hanna Krasowski^*, and Murat Arcak

   2026

   Abs arXiv

   Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable sets and derives probabilistic guarantees directly from data. Several popular techniques for validating reachable sets – conformal prediction, scenario optimization, and the holdout method – admit similar Probably Approximately Correct (PAC) guarantees. We establish a formal connection between these PAC bounds and present an empirical case study on reachable sets to illustrate the computational and sample trade-offs associated with these methods. We argue that despite the formal relationship between these techniques, subtle differences arise in both the interpretation of guarantees and the parameterization. As a result, these methods are not generally interchangeable. We conclude with practical advice on the usage of these methods.

2. 

   Importance Sampling for Statistical Certification of Viable Initial Sets

   Elizabeth Dietrich, Hanna Krasowski, Vegard Flovik, and 1 more author

   2026

   Abs arXiv

   We study the problem of statistically certifying viable initial sets (VISs) – sets of initial conditions whose trajectories satisfy a given control specification. While VISs can be obtained from model-based methods, these methods typically rely on simplified models. We propose a simulation-based framework to certify VISs by estimating the probability of specification violations under a high-fidelity or black-box model. Since detecting these violations may be challenging due to their scarcity, we propose a sample-efficient framework that leverages importance sampling to target high-risk regions. We derive an empirical Bernstein inequality for weighted random variables, enabling finite-sample guarantees for importance sampling estimators. We demonstrate the effectiveness of the proposed approach on two systems and show improved convergence of the resulting bounds on an Adaptive Cruise Control benchmark.

3. 

   Finite-Step Invariant Sets for Hybrid Systems with Probabilistic Guarantees

   Varun Madabushi^*, Elizabeth Dietrich^*, Hanna Krasowski, and 1 more author

   2026

   Abs arXiv

   Poincare return maps are a fundamental tool for analyzing periodic orbits in hybrid dynamical systems, including legged locomotion, power electronics, and other cyber-physical systems with switching behavior. The Poincare return map captures the evolution of the hybrid system on a guard surface, reducing the stability analysis of a periodic orbit to that of a discrete-time system. While linearization provides local stability information, assessing robustness to disturbances requires identifying invariant sets of the state space under the return dynamics. However, computing such invariant sets is computationally difficult, especially when system dynamics are only available through forward simulation. In this work, we propose an algorithmic framework leveraging sampling-based optimization to compute a finite-step invariant ellipsoid around a nominal periodic orbit using sampled evaluations of the return map. The resulting solution is accompanied by probabilistic guarantees on finite-step invariance satisfying a user-defined accuracy threshold. We demonstrate the approach on two low-dimensional systems and a compass-gait walking model.

2025

1. 

   pacSTL: PAC-Bounded Signal Temporal Logic from Data-Driven Reachability Analysis

   Elizabeth Dietrich^*, Hanna Krasowski^*, Emir Cem Gezer, and 3 more authors

   2025

   Abs arXiv Video

   Real-world robotic systems must comply with safety requirements in the presence of uncertainty. To define and measure requirement adherence, Signal Temporal Logic (STL) offers a mathematically rigorous and expressive language. However, standard STL cannot account for uncertainty. We address this problem by presenting pacSTL, a framework that combines Probably Approximately Correct (PAC) bounded set predictions with an interval-extension of STL through optimization problems on the atomic proposition level. pacSTL provides PAC-bounded robustness intervals on the specification level that can be utilized in monitoring. We demonstrate the effectiveness of this approach through maritime navigation and analyze the efficiency and scalability of pacSTL through simulation and real-world experimentation on model vessels.

published

2025

1. 

   Data-Driven Reachability with Scenario Optimization and the Holdout Method

   Elizabeth Dietrich, Rosalyn Devonport, Stephen Tu, and 1 more author

   In 2025 IEEE 64th Conference on Decision and Control (CDC), 2025

   Abs Bib PDF

   Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional systems, recent work has focused on the use of probabilistic methods for computing approximate reachable sets. In this work, we advocate for the use of a general purpose, practical, and sharp method for data-driven reachability: the holdout method. Despite the simplicity of the holdout method, we show—on several numerical examples including scenario-based reach tubes—that the resulting probabilistic bounds are substantially sharper and require fewer samples than existing methods for data-driven reachability. Furthermore, we complement our work with a discussion on the necessity of probabilistic reachability bounds. We argue that any method that attempts to de-randomize the bounds, by converting the guarantees to hold deterministically, requires (a) an exponential in state-dimension amount of samples to achieve non-vacuous guarantees, and (b) extra assumptions on the dynamics.

   @inproceedings{Dietrich2025_a,
     author = {Dietrich, Elizabeth and Devonport, Rosalyn and Tu, Stephen and Arcak, Murat},
     booktitle = {2025 IEEE 64th Conference on Decision and Control (CDC)},
     title = {Data-Driven Reachability with Scenario Optimization and the Holdout Method},
     year = {2025},
     volume = {},
     number = {},
     pages = {3925-3931},
     keywords = {Probabilistic logic;Safety;Computational efficiency;Complexity theory;Reachability analysis;Optimization},
     url = {https://ieeexplore.ieee.org/document/11312065}
   }

2. 

   Symbolic Control for Autonomous Docking of Marine Surface Vessels

   Elizabeth Dietrich^*, Emir Cem Gezer^*, Bingzhuo Zhong, and 4 more authors

   In 2025 IEEE 64th Conference on Decision and Control (CDC), 2025

   Abs Bib PDF Video

   Docking marine surface vessels remains a largely manual task due to its safety-critical nature. In this paper, we develop a hierarchical symbolic control architecture for autonomous docking maneuvers of a dynamic positioning vessel, to provide formal safety guarantees. At the upper-level, we treat the vessel’s desired surge, sway, and yaw velocities as control inputs and synthesize a symbolic controller in real-time. The desired velocities are then transmitted to and executed by the vessel’s low-level velocity feedback control loop. Given a synthesized symbolic controller, we investigate methods to optimize the performance of the proposed control scheme for the docking task. The efficacy of this methodology is evaluated on a low-fidelity simulation model of a marine surface vessel in the presence of static and dynamic obstacles and, for the first time, through physical experiments on a scaled model vessel.

   @inproceedings{Dietrich2025_b,
     author = {Dietrich, Elizabeth and Gezer, Emir Cem and Zhong, Bingzhuo and Arcak, Murat and Zamani, Majid and Skjetne, Roger and Sørensen, Asgeir Johan},
     booktitle = {2025 IEEE 64th Conference on Decision and Control (CDC)},
     title = {Symbolic Control for Autonomous Docking of Marine Surface Vessels},
     year = {2025},
     volume = {},
     number = {},
     pages = {3021-3026},
     keywords = {Computational modeling;Graphics processing units;Computer architecture;Parallel processing;Real-time systems;Safety;Feedback control;Surges},
     url = {https://ieeexplore.ieee.org/document/11312758}
   }

2024

1. 

   Nonconvex scenario optimization for data-driven reachability

   Elizabeth Dietrich, Alex Devonport, and Murat Arcak

   In Proceedings of the 6th Annual Learning for Dynamics & Control Conference, 2024

   Abs Bib PDF

   Many of the popular reachability analysis methods rely on the existence of system models. When system dynamics are uncertain or unknown, data-driven techniques must be utilized instead. In this paper, we propose an approach to data-driven reachability that provides a probabilistic guarantee of correctness for these systems through nonconvex scenario optimization. We pose the problem of finding reachable sets directly from data as a chance-constrained optimization problem, and present two algorithms for estimating nonconvex reachable sets: (1) through the union of partition cells and (2) through the sum of radial basis functions. Additionally, we investigate numerical examples to demonstrate the capability and applicability of the introduced methods to provide nonconvex reachable set approximations.

   @inproceedings{Dietrich2024,
     title = {Nonconvex scenario optimization for data-driven reachability},
     author = {Dietrich, Elizabeth and Devonport, Alex and Arcak, Murat},
     booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference},
     year = {2024},
     url = {https://proceedings.mlr.press/v242/dietrich24a.html}
   }