Related papers: Distributionally Robust Profit Opportunities
A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…
Distributional ambiguity sets provide quantifiable ways to characterize the uncertainty about the true probability distribution of random variables of interest. This makes them a key element in data-driven robust optimization by exploiting…
Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…
The effects of treatments are often heterogeneous, depending on the observable characteristics, and it is necessary to exploit such heterogeneity to devise individualized treatment rules (ITRs). Existing estimation methods of such ITRs…
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible 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…
Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard…
In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method…
Safety assurance is uncompromisable for safety-critical environments with the presence of drastic model uncertainties (e.g., distributional shift), especially with humans in the loop. However, incorporating uncertainty in safe learning will…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
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 use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
In this paper, we investigate distributionally robust model order reduction for linear, discrete-time, time-invariant systems. The external input is assumed to follow an uncertain distribution within a Wasserstein ambiguity set. We begin by…
We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…
We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our…
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…
We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…