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We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
In this paper we approximate high-dimensional functions $f\colon\mathbb T^d\to\mathbb C$ by sparse trigonometric polynomials based on function evaluations. Recently it was shown that a dimension-incremental sparse Fourier transform (SFT)…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained…
In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…
This paper studies stabilization of linear time-invariant (LTI) systems when control actions can only be realized in finitely many directions where it is possible to actuate uniformly or logarithmically extended positive scaling factors in…
We consider the maximal reach-avoid probability to a target in finite horizon for semi-Markov decision processes with time-varying obstacles. Since the variance of the obstacle set, the model \eqref{Model} is non-homogeneous. To overcome…
In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
Estimating rare events in complex systems is a key challenge in reliability analysis. The challenge grows in multimodal problems, where traditional methods often rely on a small set of design points and risk overlooking critical failure…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can…
In many human-in-the-loop robotic applications such as robot-assisted surgery and remote teleoperation, predicting the intended motion of the human operator may be useful for successful implementation of shared control, guidance virtual…
In this paper, we compare several representative barrier-like conditions from the literature for infinite-horizon reach-avoid verification of stochastic discrete-time systems. Our comparison examines both their theoretical properties and…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…
In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both…
We study the multi-stage stochastic unit commitment problem in which commitment and generation decisions can be made and adjusted in each time period. We formulate this problem as a Markov decision process, which is "weakly-coupled" in the…