Residuals-based distributionally robust optimization with covariate information

Distributionally Robust Expected Residual Minimization for Stochastic Variational Inequality Problems

The stochastic variational inequality problem (SVIP) is an equilibrium model that includes random variables and has been widely applied in various fields such as economics and engineering. Expected residual minimization (ERM) is an established model for obtaining a reasonable solution for the SVIP, and its objective function is an expected value of a suitable merit function for the SVIP. However, the ERM is restricted to the case where the distribution is known in advance. We extend the ERM to ensure the attainment of robust solutions for the SVIP under the uncertainty distribution (the extend…

Distributionally robust stochastic programs with side information based on trimmings -- Extended version

We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsic error in the process of inferring conditional information from limited joint data. We show that our …

基于残差的上下文分布鲁棒优化与决策依赖不确定性：理论保证与分解算法

Residuals-Based Contextual Distributionally Robust Optimization with Decision-Dependent Uncertainty: Theoretical Guarantees and Decomposition Algorithm

本文提出了一种基于残差的分布鲁棒优化模型，考虑了不确定性依赖于协变量信息和决策的情况，通过参数和非参数回归模型学习决策依赖性，并利用经验残差构建名义分布，利用Wasserstein距离定义模糊集，提供满足渐近最优性、收敛速度和有限样本保证的条件，并开发了专用的Bender分解算法求解模型。

Distributionally Robust Prescriptive Analytics with Wasserstein Distance

In prescriptive analytics, the decision-maker observes historical samples of $(X, Y)$, where $Y$ is the uncertain problem parameter and $X$ is the concurrent covariate, without knowing the joint distribution. Given an additional covariate observation $x$, the goal is to choose a decision $z$ conditional on this observation to minimize the cost $\mathbb{E}[c(z,Y)|X=x]$. This paper proposes a new distributionally robust approach under Wasserstein ambiguity sets, in which the nominal distribution of $Y|X=x$ is constructed based on the Nadaraya-Watson kernel estimator concerning the historical dat…

Distributionally robust model predictive control for wind farms

In this paper, we develop a distributionally robust model predictive control framework for the control of wind farms with the goal of power tracking and mechanical stress reduction of the individual wind turbines. We introduce an ARMA model to predict the turbulent wind speed, where we merely assume that the residuals are sub-Gaussian noise with statistics contained in an moment-based ambiguity set. We employ a recently developed distributionally model predictive control scheme to ensure constraint satisfaction and recursive feasibility of the control algorithm. The effectiveness of the approa…

Statistical Analysis of Wasserstein Distributionally Robust Estimators

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 from limited samples, the min-max formulations introduce an adversarial inner player to explore unseen covariate data. The resulting Distributionally Robust Optimization (DRO) formulations, which include Wasserstein DRO formulations (our main focus), are specified using optimal transportation phenomena. Upon describing how these infinite-dimensional min-max…