Related papers: Wasserstein Two-Sided Chance Constraints with An A…
The growing amount of fluctuating renewable infeeds and market liberalization increases uncertainty in power system operation. To capture the influence of fluctuations in operational planning, we model the forecast errors of the uncertain…
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…
Due to the increasing amount of electricity generated from renewable sources, uncertainty in power system operation will grow. This has implications for tools such as Optimal Power Flow (OPF), an optimization problem widely used in power…
Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain…
In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…
Certified robustness in machine learning has primarily focused on adversarial perturbations of the input with a fixed attack budget for each point in the data distribution. In this work, we present provable robustness guarantees on the…
Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, offering global optimality through its convex formulation. The safe corridor is constructed based on the…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
The uncertainty of multiple power loads and renewable energy generations (PLREG) in power systems increases the complexity of power flow analysis for decision-makers. The chance-constrained method can be applied to model the optimization…
This paper considers a risk-constrained motion planning problem and aims to find the solution combining the concepts of iterative model predictive control (MPC) and data-driven distributionally robust (DR) risk-constrained optimization. In…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…
Safety-critical control systems, such as spacecraft performing proximity operations, must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. Although Control Barrier Functions…
Two common problems in time series analysis are the decomposition of the data stream into disjoint segments that are each in some sense "homogeneous" - a problem known as Change Point Detection (CPD) - and the grouping of similar…
Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a…
This paper proposes a unit commitment (UC) model based on data-driven Wasserstein distributionally robust optimization (WDRO) for power systems under uncertainty of renewable generation as well as its tractable exact reformulation. The…
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…
Barycenter problems encode important geometric information about a metric space. While these problems are typically studied with positive weight coefficients associated to each distance term, more general signed Wasserstein barycenter…
To figure out the stability issues brought by renewable energy sources (RES) with non-Gaussian uncertainties in isolated microgrids, this paper proposes a chance constrained stability constrained optimal power flow (CC-SC-OPF) model.…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…