Related papers: Optimized Dimensionality Reduction for Moment-base…

Distributionally robust optimization (DRO) is a worst-case framework for stochastic optimization under uncertainty that has drawn fast-growing studies in recent years. When the underlying probability distribution is unknown and observed…

It is essential to capture the true probability distribution of uncertain data in the distributionally robust optimization (DRO). The uncertain data presents multimodality in numerous application scenarios, in the sense that the probability…

Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…

Group distributionally robust optimization (GDRO) aims to develop models that perform well across $m$ distributions simultaneously. Existing GDRO algorithms can only process a fixed number of samples per iteration, either 1 or $m$, and…

Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide…

The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…

This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…

Topology design is a critical task for the reliability, economic operation, and resilience of distribution systems. This paper proposes a distributionally robust optimization (DRO) model for designing the topology of a new distribution…

We consider a residuals-based distributionally robust optimization (DRO) model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt both parametric and nonparametric regression models to learn…

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…

In this paper, we consider a distributionally robust resource planning model inspired by a real-world service industry problem. In this problem, there is a mixture of known demand and uncertain future demand. Prior to having full knowledge…

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…

Large Language Model-based Dense Retrieval (LLM-DR) optimizes over numerous heterogeneous fine-tuning collections from different domains. However, the discussion about its training data distribution is still minimal. Previous studies rely…

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…

In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

Distributionally Robust Optimization (DRO) has been shown to provide a flexible framework for decision making under uncertainty and statistical estimation. For example, recent works in DRO have shown that popular statistical estimators can…

orthoDr is a package in R that solves dimension reduction problems using orthogonality constrained optimization approach. The package serves as a unified framework for many regression and survival analysis dimension reduction models that…

We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…

In this paper, we propose several new stochastic second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration, making them computationally efficient and comparable to policy…