Related papers: Distributional robustness in minimax linear quadra…

This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…

Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine…

This paper studies a discrete-time stochastic control problem with linear quadratic criteria over an infinite-time horizon. We focus on a class of control systems whose system matrices are associated with random parameters involving unknown…

We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…

We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this…

We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…

K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a…

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…

We study the approximation of a (finite) continuous-time Markov chain by a Markov chain on a reduced state space, and we provide formal error bounds for the approximated transient distributions in the Wasserstein distance. These bounds…

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

We study model predictive control (MPC) problems for stochastic LTI systems, where the noise distribution is unknown, compactly supported, and only observable through a limited number of i.i.d. noise samples. Building upon recent results in…

Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC)…

We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…

This paper proposes an iterative distributionally robust model predictive control (MPC) scheme to solve a risk-constrained infinite-horizon optimal control problem. In each iteration, the algorithm generates a trajectory from the starting…

We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from…

Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…

We study the problem of robust distribution estimation under the Wasserstein distance, a popular discrepancy measure between probability distributions rooted in optimal transport (OT) theory. Given $n$ samples from an unknown distribution…

Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs…

Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We address this problem through the principled lens of distributionally robust optimization, which guarantees…