Related papers: Wasserstein Distributionally Robust Stochastic Con…

There are numerous industrial settings in which a decision maker must decide whether to enter into long-term contracts to guarantee price (and hence cash flow) stability or to participate in more volatile spot markets. In this paper, we…

We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…

We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…

This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian.…

Distributionally Robust Optimization (DRO) has enabled to prove the equivalence between robustness and regularization in classification and regression, thus providing an analytical reason why regularization generalizes well in statistical…

The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting…

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional uncertainty using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are…

We consider the problem of direct data-driven predictive control for unknown stochastic linear time-invariant (LTI) systems with partial state observation. Building upon our previous research on data-driven stochastic control, this paper…

Precise control under uncertainty requires a good understanding and characterization of the noise affecting the system. This paper studies the problem of steering state distributions of dynamical systems subject to partially known…

Using only retrospective data, we study the problem of predicting treatment effects for the same treatment/policy implemented in a different location or time period. We propose a distributionally robust estimator that minimizes the…

The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…

We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…

The main goal of this paper is to discuss the construction of distributionally robust counterparts of stochastic optimal control problems. Randomized and non-randomized policies are considered. In particular, necessary and sufficient…

In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under…

Adversarially robust optimization (ARO) has emerged as the *de facto* standard for training models that hedge against adversarial attacks in the test stage. While these models are robust against adversarial attacks, they tend to suffer…

In this paper, we propose a data-based methodology to solve a multi-period stochastic optimal water flow (OWF) problem for water distribution networks (WDNs). The framework explicitly considers the pump schedule and water network head level…