Season 5 

Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this talk, we propose new reformulation techniques for adaptive robust binary optimization (ARBO) problems with objective uncertainty. Our main contribution revolves around a collection of exact and approximate network flow reformulations for the ARBO problem, which we develop by building upon ideas from the decision diagram literature. Our proposed models can generate feasible solutions, primal bounds and dual bounds, while their size and approximation quality can be precisely controlled through user-specified parameters. Furthermore, these models are easy to implement and can be solved directly with standard off-the-shelf solvers. We show that our models can generate high-quality solutions and dual bounds in significantly less time than popular benchmark methods.

Ian Zhu is an Assistant Professor in the Department of Analytics and Operations at NUS Business School. His research interests broadly lie in the design of algorithms for solving various optimization problems. His research has been published in journals such as Operations Research, MSOM, and INFORMS Journal on Computing, and has been recognized in several paper awards, including the Pierskalla Best Paper Award, Innovative Applications in Analytics Award, and the MSOM Student Paper Competition.

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, we consider a generalization of the discrete-time, finite-horizon LQG problem, where the noise distributions are unknown and belong to Wasserstein ambiguity sets centered at nominal (Gaussian) distributions. The objective is to minimize a worst-case cost across all distributions in the ambiguity set, including non-Gaussian distributions. Despite the added complexity, we prove that a control policy that is linear in the observations is optimal for this problem, as in the classic LQG problem. We propose a numerical solution method that efficiently characterizes this optimal control policy. Our method uses the Frank-Wolfe algorithm to identify the least-favorable distributions within the Wasserstein ambiguity sets and computes the controller's optimal policy using Kalman filter estimation under these distributions.

Bahar is an Assistant Professor of Operations Management at the University of Chicago Booth School of Business. In 2024, she completed her PhD in the Risk Analytics and Optimization Lab at École polytechnique fédérale de Lausanne (EPFL) in Switzerland. In 2018, she obtained her Bachelor of Science degree in Electrical and Electronics Engineering from the Middle East Technical University.

This talk presents two approaches to addressing multistage optimization problems under uncertainty: multistage robust optimization (RO) and multistage distributionally robust optimization (DRO).

In the first part of the talk, we focus on multistage robust optimization problems of the minimax type, where the uncertainty set is modeled as a Cartesian product of compact stagewise sets [1]. To manage the inherent intractability of these problems, we propose an approximation strategy based on random sampling of the uncertainty space. This leads to two main questions: (1) how to quantify the error introduced by this sampling approach as a function of the sample size, and (2) whether the optimal value of the sampled problem converges to the true robust optimal value as the number of samples increases. We provide probabilistic guarantees on constraint violations and develop a sequence of lower bounds for the original robust problem. Numerical results on a multistage inventory management problem show that the method is effective for problems with a small number of stages, while highlighting computational limitations for larger-scale instances.

The second part of the talk focuses on multistage mixed-integer distributionally robust optimization. In this setting, uncertainty is represented through conditional ambiguity sets defined on scenario trees, constrained to remain close to nominal conditional distributions according to some measure of similarity/distance. 

We propose a new bounding technique based on scenario grouping using the ambiguity sets associated

with various commonly used φ-divergences and the Wasserstein distance [2]. Our approach does not rely on specific structural assumptions such as linearity, convexity, or stagewise independence. The resulting bounds are applicable to a wide variety of DRO problems - multistage or two-stage, with or without integer variables, convex or nonconvex. Numerical results on a multistage production planning problem illustrate the effectiveness of the approach across different ambiguity sets, robustness levels, and partition strategies.

This talk aims to provide theoretical insights and practical methods for tackling uncertainty in multistage optimization, highlighting key aspects of both robust and distributionally robust formulations.

References:

[1] Maggioni, F., Dabbene, & Pflug, G. (2025) Multistage robust convex optimization problems: A sampling based approach, Annals of Operations Research, https://doi.org/10.1007/s10479-025-06545-4.

[2] Bayraksan, G., Maggioni, F., Faccini, D. & Yang, A. (2024) Bounds for Multistage Mixed-Integer Distributionally Robust Optimization, Siam Journal on Optimization, 34(1), 682-717.

Francesca Maggioni is Professor of Operations Research at the Department of Management, Information and Production Engineering (DIGIP) of the University of Bergamo (Italy). Her research interests concern both methodological and applicative aspects for optimization under uncertainty. From a methodological point of view, she has developed different types of bounds and approximations for stochastic, robust and distributionally robust multistage optimization problems. She applies these methods to solve problems in logistics, transportation, energy and machine learning. On these topics she has published more than 80 scientific articles featured in peer-reviewed operations research journals. In 2021 her research has been supported as principal investigator by a grant from the Italian Ministry of Education for the project “ULTRA OPTYMAL Urban Logistics and sustainable TRAnsportation: OPtimization under uncertainTY and MAchine Learning”. 

She is currently coordinating the research group CQIIA-Matnet for teaching of mathematics and its applications of the University of Bergamo and is Deputy Director of the PhD program in Applied Economics & Management of the Universities of Bergamo and Pavia.

She currently chairs the EURO Working Group on Stochastic Optimization and the AIRO Thematic Section of Stochastic Programming. She has been secretary and treasurer of the Stochastic Programming Society. She is Associate Editor of the journals Transportation Science, Computational Management Science (CMS), EURO Journal on Computational Optimization (EJCO), TOP, International Transactions in Operational Research (ITOR), Networks, RAIRO Operations Research and guest editor of several special issues in Operations Research and Applied Mathematics journals.

The utilization of data is becoming paramount in addressing modern, increasingly complex, optimization problems. In this talk, I will present my vision of key aspects relating to data-driven robust optimization: (i) should data be used to first construct a description of uncertainty, or should we rather use data directly in the optimization domain? (ii) is it possible to endow data-driven designs with robustness certificates that hold without any a-priori knowledge? In the second part of the talk, I will introduce “Scenario Optimization”, a collection of data-driven optimization techniques that can provide algorithmic and theoretical answers to these questions.  

Marco C. Campi is Professor of Control and Data-Driven Methods at the University of Brescia, Italy. He has held visiting and teaching appointments with Australian, USA, Japanese, Indian, Turkish and various European universities, besides the NASA Langley Research Center in Hampton, Virginia, USA. He has served as Chair of multiple IFAC Technical Committees and has been in diverse capacities on the Editorial Board of top-tier control and optimization journals. In 2008, he received the IEEE CSS George S. Axelby award for the article “The Scenario Approach to Robust Control Design”. He has delivered plenary and semi-plenary addresses at major conferences including OPTIMIZATION, SYSID, and CDC, besides presenting various talks as IEEE distinguished lecturers for the Control Systems Society. Marco C. Campi is a Fellow of IEEE and a Fellow of IFAC. His interests include: data-driven decision-making, stochastic optimization, inductive methods, and the fundamentals of probability theory. 

Counterfactual explanations (CEs) are advocated as being ideally suited to providing algorithmic recourse for subjects affected by the predictions of machine learning models. While CEs can be beneficial to affected individuals, recent work has exposed severe issues related to the robustness of state-of-the-art methods for obtaining CEs. Since a lack of robustness may compromise the validity of CEs, techniques to mitigate this risk are in order. In this talk we will begin by introducing the problem of (lack of) robustness, discuss its implications and present some recent solutions we developed to compute CEs with robustness guarantees.

Francesco is a Research Fellow affiliated with the Centre for Explainable Artificial Intelligence at Imperial College London. His research focuses on safe and explainable AI, with special emphasis on counterfactual explanations and their robustness. Since 2022, he leads the project “ConTrust: Robust Contrastive Explanations for Deep Neural Networks”, a four-year effort devoted to the formal study of robustness issues arising in XAI. More details about Francesco and his research can be found at https://fraleo.github.io/.

Sequential decision making often requires dynamic policies, which are computationally not tractable in general. Decision rules provide approximate solutions by restricting decisions to simple functions of uncertainties. In this paper, we consider a nonparametric lifting framework where the uncertainty space is lifted to higher dimensions to obtain nonlinear decision rules. We propose two nonparametric liftings, which derive the nonlinear functions by leveraging the uncertainty set structure and problem coefficients. Both methods integrate the benefits from lifting and nonparametric approaches, and hence provide scalable decision rules with performance bounds. More specifically, the set-driven lifting is constructed by finding polyhedrons within uncertainty sets, inducing piecewise-linear decision rules with performance bounds. The dynamics-driven lifting, on the other hand, is constructed by extracting geometric information and accounting for problem coefficients. This is achieved by using linear decision rules of the original problem, also enabling one to quantify lower bounds of objective improvements over linear decision rules. Numerical comparisons with competing methods demonstrate superior computational scalability and comparable performance in objectives. These observations are magnified in multistage problems with extended time horizons, suggesting practical applicability of the proposed nonparametric liftings in large-scale dynamic robust optimization.

Eojin Han is an assistant professor of IT, Analytics and Operations in Mendoza College of Business at University of Notre Dame. His research focuses on developing robust optimization methods to address operational challenges arising from uncertainties where accurate predictions are not available, with applications to healthcare, supply chains, and service systems. His work has been published in leading academic journals such as Operations Research and Management Science. Before joining Notre Dame, he served as an assistant professor at Southern Methodist University. Dr. Han holds a Ph.D. in Industrial Engineering and Management Sciences from Northwestern University and a B.S. in Mathematics and Electrical Engineering from Seoul National University. 

In bilevel and robust optimization we are concerned with combinatorial min-max problems, for example from the areas of min-max regret robust optimization, network interdiction, most vital vertex problems, blocker problems, and two-stage adjustable robust optimization.

Even though these areas are well-researched for over two decades and one would naturally expect many (if not most) of the problems occurring in these areas to be complete for the classes \Sigma_2 or \Sigma_3  from the polynomial hierarchy, almost no hardness results in this regime are currently known.

However, such complexity insights are important, since they imply that no polynomial-sized integer program for these min-max problems exist (unless the polynomial hierarchy collapses), and hence conventional IP-based approaches fail.

We address this lack of knowledge by introducing over 70 new \Sigma_2-complete and \Sigma_3-complete problems. I particular, we explore a meta-theorem, which reveals an underlying pattern behind the computational hardness of combinatorial min-max problems. Our meta-theorem applies to many classic combinatorial problems (like TSP, clique, vertex cover, facility location, knapsack, etc...) in conjunction with min-max regret, network interdiction, or two-stage adjustable robust optimization.

Lasse Wulf is a postdoctoral researcher at the Technical University of Denmark (DTU). He obtained a double master's degree in mathematics and computer science from Karlsruhe Institute of Technology (KIT) and a PhD from the Technical University of Graz. He is recipient of the best student paper award at IWOCA 2021, and the best dissertation award from the Austrian Society of Operations Research (ÖGOR). His research in robust optimization is centered around the computational complexity of combinatorial min-max optimization, for example in min-max regret, network interdiction, bilevel, and adjustable/recoverable multi-stage robust optimization. In particular, he is interested in cases where such problems are even harder than NP-hard.

In this talk, we first briefly review a general class of data-driven decision-making and highlight the role of convexity in addressing three research questions that arise in this context. We then focus on a particular setting of such problems known as inverse optimization (IO), where the goal is to replicate the behavior of a decision-maker with an unknown objective function. We discuss recent developments in IO concerning convex training losses and optimization algorithms. The main message of this talk is that IO is a rich supervised learning model that can capture a complex (e.g., discontinuous) behavior while the training phase is still a convex program. We motivate the discussion with applications from control (learning the MPC control law), transportation (the 2021 Amazon Routing Problem Challenge), and robotics (comparison with the state-of-the-art in the MuJoCo environments).    

Peyman Mohajerin Esfahani is an Associate Professor at the Delft Center for Systems and Control. He joined TU Delft in October 2016, and prior to that, he held several research appointments at EPFL, ETH Zurich, and MIT between 2014 and 2016. He received the BSc and MSc degrees from Sharif University of Technology, Iran, and the PhD degree from ETH Zurich. He currently serves as an associate editor of Mathematical Programming, Operations Research, Transactions on Automatic Control, and Open Journal of Mathematical Optimization. He was one of the three finalists for the Young Researcher Prize in Continuous Optimization awarded by the Mathematical Optimization Society in 2016, and a recipient of the 2016 George S. Axelby Outstanding Paper Award from the IEEE Control Systems Society. He received the ERC Starting Grant and the INFORMS Frederick W. Lanchester Prize in 2020. He is the recipient of the 2022 European Control Award.