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Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach for comparing uncertain quantities, but optimization with stochastic dominance constraints is…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…
In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of…
Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
The LATIN method has been developed and successfully applied to a variety of deterministic problems, but few work has been developed for nonlinear stochastic problems. This paper presents a stochastic LATIN method to solve stochastic and/or…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…