Related papers: A General Wasserstein Framework for Data-driven Di…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the…
In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
This paper provides a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the distributional uncertainties to the chance probabilities. Our analysis allows a decision-maker to interpret the size…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
Asset Liability Management (ALM) represents a fundamental challenge for financial institutions, particularly pension funds, which must navigate the tension between generating competitive investment returns and ensuring the solvency of…
In recent years, there has been a growing research interest in decision-focused learning, which embeds optimization problems as a layer in learning pipelines and demonstrates a superior performance than the prediction-focused approach.…
Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
In the optimization under uncertainty, decision-makers first select a wait-and-see policy before any realization of uncertainty and then place a here-and-now decision after the uncertainty has been observed. Two-stage stochastic programming…
This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions…
Multivariate time series imputation is often compromised by mismatch between the observed and true data distributions, a bias induced by the combined effects of time-series non-stationarity and systematic missingness. Standard methods that…
Modern machine learning models may be susceptible to learning spurious correlations that hold on average but not for the atypical group of samples. To address the problem, previous approaches minimize the empirical worst-group risk. Despite…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event…
Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the…
In federated learning, participating clients typically possess non-i.i.d. data, posing a significant challenge to generalization to unseen distributions. To address this, we propose a Wasserstein distributionally robust optimization scheme…
This paper presents a distributionally robust Q-Learning algorithm (DrQ) which leverages Wasserstein ambiguity sets to provide idealistic probabilistic out-of-sample safety guarantees during online learning. First, we follow past work by…