arXiv subjects

Sadegh Soudjani

Publications and source records attributed to Sadegh Soudjani.

At least 37 records · Page 2Linked to original sources

arXiv2026

Stochastic Generalized Dynamic Games with Coupled Chance Constraints

This paper investigates stochastic generalized dynamic games with coupling chance constraints, where agents have incomplete information about uncertainties satisfying a concentration of measure property. This problem, in general, is non-convex and NP-hard. To address this, we propose a convex under-approximation by replacing chance constraints with tightened expected-value constraints, yielding a tractable game. We prove the existence of a stochastic generalized Nash equilibrium (SGNE) in this new game and show that its variational SGNE is an $\boldsymbol{\varepsilon}$-SGNE for the original game, with $\boldsymbol{\varepsilon}$ expressed via the approximation errors and Lagrange multipliers. A semi-decentralized, sampling-based algorithm with time-varying step sizes is developed, requiring no prior knowledge of the uncertainty distribution or expectation evaluations. Unlike existing methods, it avoids step-size tuning based on Lipschitz constants or adaptive rules. Under standard assumptions on the pseudo-gradient, the algorithm converges almost surely to an SGNE.

eess.SY↗

arXiv2026

Kernel-Based Learning of Safety Barriers

The rapid integration of AI algorithms in safety-critical applications such as autonomous driving and healthcare is raising significant concerns about the ability to meet stringent safety standards. Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems and lack the flexibility needed to scale to the complexity of real-world applications. In this paper, we present a data-driven approach for safety verification and synthesis of black-box systems with discrete-time stochastic dynamics. We employ the concept of control barrier certificates, which can guarantee safety of the system, and learn the certificate directly from a set of system trajectories. We use conditional mean embeddings to embed data from the system into a reproducing kernel Hilbert space (RKHS) and construct an RKHS ambiguity set that can be inflated to robustify the result to out-of-distribution behavior. We provide the theoretical results on how to apply the approach to general classes of temporal logic specifications beyond safety. For the data-driven computation of safety barriers, we leverage a finite Fourier expansion to cast a typically intractable semi-infinite optimization problem as a linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. Our work moves beyond restrictive assumptions on system dynamics and uncertainty, as demonstrated on two case studies including a black-box system with a neural network controller.

cs.AI↗

arXiv2026

Policy Synthesis for Interval MDPs via Polyhedral Lyapunov Functions

Decision-making under uncertainty is central to many safety-critical applications, where decisions must be guided by probabilistic modeling formalisms. This paper introduces a novel approach to policy synthesis in multi-objective interval Markov decision processes using polyhedral Lyapunov functions. Unlike previous Lyapunov-based methods that mainly rely on quadratic functions, our method utilizes polyhedral functions to enhance accuracy in managing uncertainties within value iteration of dynamic programming. We reformulate the value iteration algorithm as a switched affine system with interval uncertainties and apply control-theoretic stability principles to synthesize policies that guide the system toward a desired target set. By constructing an invariant set of attraction, we ensure that the synthesized policies provide convergence guarantees while minimizing the impact of transition uncertainty in the underlying model. Our methodology removes the need for computationally intensive Pareto curve computations by directly determining a policy that brings objectives within a specified range of their target values. We validate our approach through numerical case studies, including a recycling robot and an electric vehicle battery, demonstrating its effectiveness in achieving policy synthesis under uncertainty.

eess.SY↗

arXiv2025

LUCID: Learning-Enabled Uncertainty-Aware Certification of Stochastic Dynamical Systems

Ensuring the safety of AI-enabled systems, particularly in high-stakes domains such as autonomous driving and healthcare, has become increasingly critical. Traditional formal verification tools fall short when faced with systems that embed both opaque, black-box AI components and complex stochastic dynamics. To address these challenges, we introduce LUCID (Learning-enabled Uncertainty-aware Certification of stochastIc Dynamical systems), a verification engine for certifying safety of black-box stochastic dynamical systems from a finite dataset of random state transitions. As such, LUCID is the first known tool capable of establishing quantified safety guarantees for such systems. Thanks to its modular architecture and extensive documentation, LUCID is designed for easy extensibility. LUCID employs a data-driven methodology rooted in control barrier certificates, which are learned directly from system transition data, to ensure formal safety guarantees. We use conditional mean embeddings to embed data into a reproducing kernel Hilbert space (RKHS), where an RKHS ambiguity set is constructed that can be inflated to robustify the result to out-of-distribution behavior. A key innovation within LUCID is its use of a finite Fourier kernel expansion to reformulate a semi-infinite non-convex optimization problem into a tractable linear program. The resulting spectral barrier allows us to leverage the fast Fourier transform to generate the relaxed problem efficiently, offering a scalable yet distributionally robust framework for verifying safety. LUCID thus offers a robust and efficient verification framework, able to handle the complexities of modern black-box systems while providing formal guarantees of safety. These unique capabilities are demonstrated on challenging benchmarks.

eess.SY↗

arXiv2025

Computation of Feasible Assume-Guarantee Contracts: A Resilience-based Approach

We propose a resilience-based framework for computing feasible assume-guarantee contracts that ensure the satisfaction of temporal specifications in interconnected discrete-time systems. Interconnection effects are modeled as structured disturbances. We use a resilience metric, the maximum disturbance under which local specifications hold, to refine assumptions and guarantees across subsystems iteratively. We first demonstrate correctness and monotone refinement of guarantees for two subsystems. Then, we extend our approach to general networks of L subsystems using weighted combinations of interconnection effects. We instantiate the framework on linear systems by meeting finite-horizon safety, exact-time reachability, and finite-horizon reachability specifications, and on nonlinear systems by fulfilling general finite-horizon specifications. Our approach is demonstrated through numerical linear examples and a nonlinear DC microgrid case study, showcasing the impact of our framework on verifying temporal logic specifications with compositional reasoning.

eess.SY↗

arXiv2025

Quasi-Newton Compatible Actor-Critic for Deterministic Policies

In this paper, we propose a second-order deterministic actor-critic framework in reinforcement learning that extends the classical deterministic policy gradient method to exploit curvature information of the performance function. Building on the concept of compatible function approximation for the critic, we introduce a quadratic critic that simultaneously preserves the true policy gradient and an approximation of the performance Hessian. A least-squares temporal difference learning scheme is then developed to estimate the quadratic critic parameters efficiently. This construction enables a quasi-Newton actor update using information learned by the critic, yielding faster convergence compared to first-order methods. The proposed approach is general and applicable to any differentiable policy class. Numerical examples demonstrate that the method achieves improved convergence and performance over standard deterministic actor-critic baselines.

cs.LG↗

arXiv2025

Second-Order Policy Gradient Methods for the Linear Quadratic Regulator

Policy gradient methods are a powerful family of reinforcement learning algorithms for continuous control that optimize a policy directly. However, standard first-order methods often converge slowly. Second-order methods can accelerate learning by using curvature information, but they are typically expensive to compute. The linear quadratic regulator (LQR) is a practical setting in which key quantities, such as the policy gradient, admit closed-form expressions. In this work, we develop second-order policy gradient algorithms for LQR by deriving explicit formulas for both the approximate and exact Hessians used in Gauss--Newton and Newton methods, respectively. Numerical experiments show a faster convergence rate for the proposed second-order approach over the standard first-order policy gradient baseline.

eess.SY↗

arXiv2025

Sum-of-Squares Certificates for Almost-Sure Reachability of Stochastic Polynomial Systems

In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite solvers. Specifically, we provide an SOS method based on two complementary certificates: (i) a drift certificate that enforces a radially unbounded function to be non-increasing in expectation outside a compact set of states; and (ii) a variant certificate that guarantees a one-step decrease with positive probability and ensures the target contains its nonpositive sublevel set. We transform these conditions to SOS constraints. For the variant condition, we enforce a robust decrease over a parameterized disturbance ball with nonzero probability and encode the constraints via an S-procedure with polynomial multipliers. The resulting bilinearities are handled by an alternating scheme that alternates between optimizing multipliers and updating the variant and radius until a positive slack is obtained. Two case studies illustrate the workflow and certifies almost-sure reachability.

math.OC↗

arXiv2025

Formal Analysis of Metastable Failures in Software Systems

Many large-scale software systems demonstrate metastable failures. In this class of failures, a stressor such as a temporary spike in workload causes the system performance to drop and, subsequently, the system performance continues to remain low even when the stressor is removed. These failures have been reported by many large corporations and considered to be a rare but catastrophic source of availability outages in cloud systems. In this paper, we provide the mathematical foundations of metastability in request-response server systems. We model such systems using a domain-specific language. We show how to construct continuous-time Markov chains (CTMCs) that approximate the semantics of the programs through modeling and data-driven calibration. We use the structure of the CTMC models to provide a visualization of the qualitative behavior of the model. The visualization is a surprisingly effective way to identify system parameterizations that cause a system to show metastable behaviors. We complement the qualitative analysis with quantitative predictions. We provide a formal notion of metastable behaviors based on escape probabilities, and show that metastable behaviors are related to the eigenvalue structure of the CTMC. Our characterization leads to algorithmic tools to predict recovery times in metastable models of server systems. We have implemented our technique in a tool for the modeling and analysis of server systems. Through models inspired by failures in real request-response systems, we show that our qualitative visual analysis captures and predicts many instances of metastability that were observed in the field in a matter of milliseconds. Our algorithms confirm that recovery times surge as the system parameters approach metastable modes in the dynamics.

cs.PF↗

arXiv2025

Maximally Resilient Controllers under Temporal Logic Specifications

In this paper, we consider the notion of resilience of a dynamical system, defined by the maximum disturbance a controlled dynamical system can withstand while satisfying given temporal logic specifications. Given a dynamical system and a specification, the objective is to synthesize the controller such that the closed-loop system satisfies this specification while maximizing its resilience. The problem is formulated as a robust optimization program where the objective is to compute the maximum resilience while simultaneously synthesizing the corresponding controller parameters. For linear systems and linear controllers, exact solutions are provided for the class of time-varying polytopic specifications. For the case of nonlinear systems, nonlinear controllers and more general specifications, we leverage tools from the scenario optimization approach, offering a probabilistic guarantee of the solution as well as computational feasibility. Different case studies are presented to illustrate the theoretical results.

eess.SY↗

arXiv2025

Data-Driven Abstraction and Synthesis for Stochastic Systems with Unknown Dynamics

We study the automated abstraction-based synthesis of correct-by-construction control policies for stochastic dynamical systems with unknown dynamics. Our approach is to learn an abstraction from sampled data, which is represented in the form of a finite Markov decision process (MDP). In this paper, we present a data-driven technique for constructing finite-state interval MDP (IMDP) abstractions of stochastic systems with unknown nonlinear dynamics. As a distinguishing and novel feature, our technique only requires (1) noisy state-input-state observations and (2) an upper bound on the system's Lipschitz constant. Combined with standard model-checking techniques, our IMDP abstractions enable the synthesis of policies that satisfy probabilistic temporal properties (such as "reach-while-avoid") with a predefined confidence. Our experimental results show the effectiveness and robustness of our approach.

eess.SY↗

arXiv2025

Data-Driven Yet Formal Policy Synthesis for Stochastic Nonlinear Dynamical Systems

The automated synthesis of control policies for stochastic dynamical systems presents significant challenges. A standard approach is to construct a finite-state abstraction of the continuous system, typically represented as a Markov decision process (MDP). However, generating abstractions is challenging when (1) the system's dynamics are nonlinear, and/or (2) we do not have complete knowledge of the dynamics. In this work, we introduce a novel data-driven abstraction technique for nonlinear Lipschitz continuous dynamical systems with additive stochastic noise that addresses both of these issues. As a key step, we use samples of the dynamics to learn the enabled actions and transition probabilities of the abstraction. We represent abstractions as MDPs with intervals of transition probabilities, known as interval MDPs (IMDPs). These abstractions enable the synthesis of policies for the concrete nonlinear system, with probably approximately correct (PAC) guarantees on the probability of satisfying a specified control objective. Our numerical experiments illustrate the effectiveness and robustness of our approach in achieving reliable control under uncertainty.

eess.SY↗

arXiv2025

On Certificates for Almost Sure Reachability in Stochastic Systems

Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure reachability in discrete-time stochastic systems using drift and variant conditions. While these conditions are both necessary and sufficient in theory, computational approaches often rely on restricting the search to fixed templates, such as polynomial or quadratic functions. We show that this restriction compromises completeness: there exists a polynomial system for which a given target set is almost surely reachable but admits no polynomial certificate, and a linear system for which a neighborhood of the origin is almost surely reachable but admits no quadratic certificate. We then provide a complete characterization of reachability certificates for linear systems with additive noise. Our analysis yields conditions on the system matrices under which valid certificates exist, and shows how the structure and dimension of the system determine the need for non-quadratic templates. Our results generalize the classical random walk behavior to a broader class of stochastic dynamical systems.

eess.SY↗

arXiv2025

Formal Control for Uncertain Systems via Contract-Based Probabilistic Surrogates (Extended Version)

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making with formal correctness and performance guarantees. Focusing on probabilistic simulation relations and surrogate models of stochastic systems, we propose an approach that significantly enhances the scalability and practical applicability of such simulation relations by eliminating the need to compute error bounds directly. As a result, we provide an abstraction-based technique that scales effectively to higher dimensions while addressing complex nonlinear agent-environment interactions with infinite-horizon temporal logic guarantees amidst uncertainty. Our approach trades scalability for conservatism favorably, as demonstrated on a complex high-dimensional vehicle intersection case study.

eess.SY↗

arXiv2025

Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach

In recent years, various techniques have been explored for the verification of quantum circuits, including the use of barrier certificates, mathematical tools capable of demonstrating the correctness of such systems. These certificates ensure that, starting from initial states and applying the system's dynamics, the system will never reach undesired states. In this paper, we propose a methodology for synthesizing such certificates for quantum circuits using a scenario-based approach, for both finite and infinite time horizons. In addition, our approach can handle uncertainty in the initial states and in the system's dynamics. We present several case studies on quantum circuits, comparing the performance of different types of barrier certificate and analyzing which one is most suitable for each case.

cs.LO↗

arXiv2025

Blending Participatory Design and Artificial Awareness for Trustworthy Autonomous Vehicles

Current robotic agents, such as autonomous vehicles (AVs) and drones, need to deal with uncertain real-world environments with appropriate situational awareness (SA), risk awareness, coordination, and decision-making. The SymAware project strives to address this issue by designing an architecture for artificial awareness in multi-agent systems, enabling safe collaboration of autonomous vehicles and drones. However, these agents will also need to interact with human users (drivers, pedestrians, drone operators), which in turn requires an understanding of how to model the human in the interaction scenario, and how to foster trust and transparency between the agent and the human. In this work, we aim to create a data-driven model of a human driver to be integrated into our SA architecture, grounding our research in the principles of trustworthy human-agent interaction. To collect the data necessary for creating the model, we conducted a large-scale user-centered study on human-AV interaction, in which we investigate the interaction between the AV's transparency and the users' behavior. The contributions of this paper are twofold: First, we illustrate in detail our human-AV study and its findings, and second we present the resulting Markov chain models of the human driver computed from the study's data. Our results show that depending on the AV's transparency, the scenario's environment, and the users' demographics, we can obtain significant differences in the model's transitions.

cs.RO↗

arXiv2025

Regret-Free Reinforcement Learning for LTL Specifications

Learning to control an unknown dynamical system with respect to high-level temporal specifications is an important problem in control theory. We present the first regret-free online algorithm for learning a controller for linear temporal logic (LTL) specifications for systems with unknown dynamics. We assume that the underlying (unknown) dynamics is modeled by a finite-state and action Markov decision process (MDP). Our core technical result is a regret-free learning algorithm for infinite-horizon reach-avoid problems on MDPs. For general LTL specifications, we show that the synthesis problem can be reduced to a reach-avoid problem once the graph structure is known. Additionally, we provide an algorithm for learning the graph structure, assuming knowledge of a minimum transition probability, which operates independently of the main regret-free algorithm. Our LTL controller synthesis algorithm provides sharp bounds on how close we are to achieving optimal behavior after a finite number of learning episodes. In contrast, previous algorithms for LTL synthesis only provide asymptotic guarantees, which give no insight into the transient performance during the learning phase.

cs.AI↗

arXiv2025

High-level quantum algorithm programming using Silq

Quantum computing, with its vast potential, is fundamentally shaped by the intricacies of quantum mechanics, which both empower and constrain its capabilities. The development of a universal, robust quantum programming language has emerged as a key research focus in this rapidly evolving field. This paper explores Silq, a recent high-level quantum programming language, highlighting its strengths and unique features. We aim to share our insights on designing and implementing high-level quantum algorithms using Silq, demonstrating its practical applications and advantages for quantum programming.

quant-ph↗