Related papers: Data-driven Reachable Set Estimation with Tunable …
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles. The…
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
We propose an explainable regime-aware portfolio construction framework based on a strictly causal Wasserstein Hidden Markov Model. The model combines rolling Gaussian HMM inference with predictive model-order selection and template-based…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard…
We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the…
In this work, we propose a new framework for reachable set computation through continuous evolution of a set of parameters and offsets which define a parametope, through the intersection of constraints. This results in a dynamical approach…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…
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…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
Finding optimal policies for Partially Observable Markov Decision Processes (POMDPs) is challenging due to their uncountable state spaces when transformed into fully observable Markov Decision Processes (MDPs) using belief states.…
We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a…
We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…