Related papers: Robust Least-Squares Optimization for Data-Driven …
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
The Linear Quadratic Gaussian (LQG) controller is known to be inherently fragile to model misspecifications common in real-world situations. We consider discrete-time partially observable stochastic linear systems and provide a…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
Recent work by Mania et al. has proved that certainty equivalent control achieves nearly optimal regret for linear systems with quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
Solving geometric optimization problems over uncertain data have become increasingly important in many applications and have attracted a lot of attentions in recent years. In this paper, we study two important geometric optimization…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…