Optimization in Data Science – Optimization Online

Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes

Published: 2026/05/28

Optimization in Data Science, Robust Optimization, Stochastic Programming Contextual optimization, corrupted and missing data, curse of dimensionality, distributionally robust optimization, heavy-tailed distributions, integral probability metrics, markovian data

Distributionally robust optimization (DRO) has been successful in addressing decision-making problems under uncertainty when the underlying distribution is unknown. Existing data-driven DRO frameworks, however, often impose restrictive assumptions on the data-generating process. We propose a new DRO framework based on targeted integral probability metrics. The ambiguity set is defined directly through the loss functions induced … Read more

Mind the Gap: Mixtures of Gaussians in Approximate Differential Privacy

Published: 2026/05/27

Huikang Liu

Aras Selvi

Wolfram Wiesemann

Optimization in Data Science differential privacy, gaussian mechanism, privacy-utility tradeoff

We design a class of additive noise mechanisms that satisfy \((\varepsilon, \delta)\)-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call \textit{mixture mechanisms}, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means … Read more

Finite-Sample Optimality and Constraint Satisfaction: Learning-Based Optimal Control in Dynamic Dispatch Networks

Published: 2026/04/30

Moustafa Rashidy

Data Science Theory, Production and Logistics, Transportation constrained optimization, nonlinear optimization, stochastic programming

Dynamic dispatch networks in logistics and transportation require real-time, constraint-aware decision-making under stochastic demand. This paper bridges mathematical optimization, optimal control theory, and reinforcement learning by establishing non-asymptotic theoretical guarantees for learning-based optimal control in constrained stochastic dispatch systems. We formulate the problem as a constrained Markov decision process, enforce feasibility via a projection-based policy … Read more

A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muon

Published: 2026/04/15, Updated: 2026/05/01

Serge Gratton

Philippe L. Toint

Data Science Algorithms, Stochastic Programming, Unconstrained Optimization adaptive first-order methods, machine learning, stochastic complexity, Unified convergence theory

A unified framework for first-order optimization algorithms for nonconvex unconstrained optimization is proposed that uses adaptively preconditioned gradients and includes popular methods such as full and diagonal AdaGrad, AdaNorm, as well as adpative variants of Shampoo and Muon. This framework also allows combining heterogeneous geometries across different groups of variables while preserving a unified convergence … Read more

An Interpretable Ensemble Heuristic for Principal-Agent Games with Machine Learning

Published: 2026/04/12

I. Esra Buyuktahtakin Toy

Applications - OR and Management Sciences, Game Theory, Optimization in Data Science

This paper addresses the challenge of enhancing public policy decision-making by efficiently solving principal-agent models (PAMs) for public-private partnerships, a critical yet computationally demanding problem. We develop a fast, interpretable, and generalizable approach to support policy decisions under these settings. We propose an interpretable ensemble heuristic (EH) that integrates Machine Learning (ML), Operations Research (OR), … 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

Bilevel Learning

Published: 2026/03/31

Alain Zemkoho

Bilevel Optimization, Optimization in Data Science bilevel learning, bilevel optimization, gradient descent method, machine learning

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine learning, as gradient-based algorithms built on the implicit function reformulation have enabled the computation of large-scale problems involving possibly millions of variables. Despite … Read more

Zeroth-Order Methods for Nonconvex-Strongly Concave Stochastic Minimax Problems with Decision-Dependent Distributions

Published: 2026/03/20

Zili Luo

Yongchao Liu

Nonlinear Optimization, Optimization in Data Science, Stochastic Programming Decision-dependent distributions, Nonconvex-strongly concave, Sample-based, Stochastic minimax problems, Zeroth-order methods

Stochastic minimax problems with decision-dependent distributions (SMDD) have emerged as a crucial framework for modeling complex systems where data distributions drift in response to decision variables. Most existing methods for SMDD rely on an explicit functional relationship between the decision variables and the probability distribution. In this paper, we propose two sample-based zeroth-order algorithms, namely … Read more

Data-driven Policies For Two-stage Stochastic Linear Programs

Published: 2026/03/17

Chhavi Sharma

Harsha Gangammanavar

Linear Programming, Optimization in Data Science, Stochastic Programming data-driven decision making, L-shaped Algorithm, stochastic decomposition, two-stage stochastic linear programs

A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes. However, in practical applications, quick decision-making is necessary, and solving a stochastic program from scratch for every change in input data can be computationally costly. This … Read more

A Projected Stochastic Gradient Method for Finite-Sum Problems with Linear Equality Constraints

Published: 2026/02/24, Updated: 2026/03/05

Nataša Krklec Jerinkić

Benedetta Morini

Mahsa Yousefi

Nonlinear Optimization, Optimization in Data Science Constrained finite-sum minimization, Exact and inexact projection, stochastic gradient

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on a convex set to the use of both a stochastic gradient and a possibly inexact projection map. Under standard assumptions in the field of stochastic gradient methods, we provide theoretical … Read more