Related papers: An optimal transport foundation for a class of dyn…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
We present a case study applying learning-based distributionally robust model predictive control to highway motion planning under stochastic uncertainty of the lane change behavior of surrounding road users. The dynamics of road users are…
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…
We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These…
We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…
Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality…
In this paper, we compare three different model-based risk measures by evaluating their stengths and weaknesses qualitatively and testing them quantitatively on a set of real longitudinal and intersection scenarios. We start with the…
We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter $\varepsilon$ tends to $0$. We establish lower and upper bounds on the difference…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
We consider weak optimal problems (possibly entropically penalized) incorporating both soft and hard (including the case of the martingale condition) moment constraints. Even in the special case of the martingale optimal transport problem,…
In this paper, we address the real-time risk-bounded safety verification problem of continuous-time state trajectories of autonomous systems in the presence of uncertain time-varying nonlinear safety constraints. Risk is defined as the…
Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding the…
This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
In this paper, we propose a data-driven robust safety verification framework for stochastic dynamical systems modeled as Markov decision processes with time-varying and uncertain transition probabilities. Rather than assuming access to the…
While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali this…
We present a method based on optimal transport to remove arbitrage opportunities within a finite set of option prices. The method is notably intended for regulatory stress-tests, which require applying significant local distortions to…
This paper proposes an iterative distributionally robust model predictive control (MPC) scheme to solve a risk-constrained infinite-horizon optimal control problem. In each iteration, the algorithm generates a trajectory from the starting…
We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions are twice continuously differentiable. We approach this optimization problem from…