Machine learning and optimization – Optimization Online

Out-of-Distribution Wasserstein Ambiguity Set Construction with Inclusive and Exclusive Evidence

Published: 2026/10/10

Biao Han

Optimization in Data Science, Robust Optimization, Stochastic Programming cognitive science, convex optimization, cutting planes, distributionally robust optimization, Machine learning and optimization, nonconvex optimization, robust optimization, stochastic programming

Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more

Robust Out-of-Distribution Stochastic Optimization Based on Wasserstein-Metric Meta-Distribution Support Learning

Published: 2026/10/05, Updated: 2026/10/08

Biao Han

Optimization in Data Science, Robust Optimization, Stochastic Programming bilevel optimization, convex optimization, data-driven stochastic programming, distributionally robust optimization, Machine learning and optimization, robust optimization

We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more

Robust Out-of-Distribution Stochastic Optimization with Heterogeneous Inclusive and Exclusive Distribution Clusters

Published: 2026/09/10, Updated: 2026/10/12

Biao Han

Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming Biconvex optimization, bilevel optimization, cognitive science, convex optimization, Data-Driven Robust Optimization, decision science, distributionally robust optimization (DRO), Machine learning and optimization, multiple kernel learning

Decision scenarios far from rare in practice often place data-driven decision-making in an awkward position, where the decision maker may have access to neither the target distribution itself nor any empirical samples drawn from it, especially when decisions must be made in novel or highly uncertain environments. In response, robust out-of-distribution stochastic optimization (RooDSO) has … Read more

Stable and Unstable Singularities in Navier-Stokes ?

Published: 2026/09/06

Orson Mengara

Nonlinear Optimization, Robust Optimization euler equations, Machine learning and optimization, Navier-Stokes equation

This document provides an extended and rigorous framework dedicated to the geometric analysis of the 3D incompressible Navier-Stokes equations \cite{ESS2003}. We comprehensively develop geometric proofs related to decay estimates, blow-up profiles, and the foundational partial regularity theory of Caffarelli, Kohn, and Nirenberg (CKN). We examine in detail the Hausdorff dimension of potential singular sets, local … Read more

Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

Published: 2026/04/12

I. Esra Buyuktahtakin Toy

Data Science Algorithms, Optimization in Data Science, Stochastic Programming decision making under uncertainty, Decision-focused learning, deep learning, learning-to-optimize, Machine learning and optimization, markov decision processes, multi-stage stochastic programming, operations research, optimization under uncertainty, reinforcement learning, sequential decision making, stochastic optimization

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management sciences (OR/MS), which have long offered conceptual and methodological foundations for sequential decision-making under uncertainty. At the same time, recent advances in deep learning, including feedforward neural … Read more