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This is the second part of a two-part paper on data-based distributionally robust stochastic optimal power flow (OPF). The general problem formulation and methodology have been presented in Part I [1]. Here, we present extensive numerical…
We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO…
We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using $f$-DRO and spectral/$L$-risk minimization. We present Drago, a stochastic…
With the ongoing investment in data collection and communication technology in power systems, data-driven optimization has been established as a powerful tool for system operators to handle stochastic system states caused by weather- and…
In this paper, we propose a risk-based data-driven approach to optimal power flow (DROPF) with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the…
We present a methodology to automatically compute worst-case performance bounds for a large class of first-order decentralized optimization algorithms. These algorithms aim at minimizing the average of local functions that are distributed…
In this paper, we consider a network capacity expansion problem in the context of telecommunication networks, where there is uncertainty associated with the expected traffic demand. We employ a distributionally robust stochastic…
This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be…
Wasserstein distributionally robust optimization (DRO) has gained prominence in operations research and machine learning as a powerful method for achieving solutions with favorable out-of-sample performance. Two compelling explanations for…
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…
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…
We focus on analyzing the classical stochastic projected gradient methods under a general dependent data sampling scheme for constrained smooth nonconvex optimization. We show the worst-case rate of convergence $\tilde{O}(t^{-1/4})$ and…
While solutions of Distributionally Robust Optimization (DRO) problems can sometimes have a higher out-of-sample expected reward than the Sample Average Approximation (SAA), there is no guarantee. In this paper, we introduce a class of…
In this work, we develop a novel data-driven Bayesian nonparametric Wasserstein distributionally robust optimization (BNWDRO) framework for decision-making under uncertainty. The proposed framework unifies a Bayesian nonparametric method…
We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of…
We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of…
This paper addresses a novel \emph{cost-sensitive} distributionally robust log-optimal portfolio problem, where the investor faces \emph{ambiguous} return distributions, and a general convex transaction cost model is incorporated. The…
Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…
Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…