Related papers: Distributional robustness in minimax linear quadra…
We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and…
The Linear Quadratic Gaussian (LQG) regulator is a cornerstone of optimal control theory, yet its performance can degrade significantly when the noise distributions deviate from the assumed Gaussian model. To address this limitation, this…
The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
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…
We revisit Merton's continuous-time portfolio selection through a data-driven, distributionally robust lens. Our aim is to tap the benefits of frequent trading over short horizons while acknowledging that drift is hard to pin down, whereas…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow notably some coefficients to be stochastic. Our method is…
The paper studies the robustness properties of discrete-time stochastic optimal control under Wasserstein model approximation for both discounted-cost and average-cost criteria. Specifically, we study the performance loss when applying an…
In the past couple of decades, non-quadratic convex penalties have reshaped signal processing and machine learning; in robust control, however, general convex costs break the Riccati and storage function structure that make the design…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…
In this paper we discuss distributional robustness in the context of stochastic model predictive control (SMPC) for linear time-invariant systems. We derive a simple approximation of the MPC problem under an additive zero-mean i.i.d. noise…
We consider a discrete time stochastic Markovian control problem under model uncertainty. Such uncertainty not only comes from the fact that the true probability law of the underlying stochastic process is unknown, but the parametric family…
We present a novel $Q$-learning algorithm tailored to solve distributionally robust Markov decision problems where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball…
We consider multiperiod stochastic control problems with non-parametric uncertainty on the underlying probabilistic model. We derive a new metric on the space of probability measures, called the adapted $(p, \infty)$--Wasserstein distance…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…