TutORials
The TutORials in Operations Research series is published annually by INFORMS as an introduction to emerging and classical subfields of operations research and management science. These chapters are designed to be accessible for all constituents of the INFORMS community, including current students, practitioners, faculty, and researchers. The publication allows readers to keep pace with new developments in the field and serves as augmenting material for a selection of the tutorial presentations offered at the INFORMS Annual Meeting.
Generative Models for Decision-Making under Distributional Shift
estimated from historical data, while performance is ultimately determined by
a deployment distribution that may be shifted, context-dependent, partially observed,
or stress-induced. This tutorial presents modern generative models, particularly flowand
score-based methods, as mathematical tools for constructing decision-relevant
distributions. From an operations research perspective, their primary value lies not
in unconstrained sample synthesis but in representing and transforming distributions
through transport maps, velocity fields, score fields, and guided stochastic dynamics.
We present a unified framework based on pushforward maps, continuity, Fokker–
Planck equations,Wasserstein geometry, and optimization in probability space.Within
this framework, generative models can be used to learn nominal uncertainty, construct
stressed or least-favorable distributions for robustness, and produce conditional or
posterior distributions under side information and partial observation. We also highlight
representative theoretical guarantees, including forward–reverse convergence for
iterative flow models, first-order minimax analysis in transport-map space, and errortransfer
bounds for posterior sampling with generative priors. The tutorial provides
a principled introduction to using generative models for scenario generation, robust
decision-making, uncertainty quantification, and related problems under distributional
shift.
Speakers: Xiuyuan Cheng, Yunqin Zhu, Yao Xie
Transform Method for Stochastic Processing and Matching Networks
Speakers: Sushil Varma, Prakirt Jhunjhunwala, Daniela Hurtado-Lange, Siva Theja Maguluri
Multi-objective Combinatorial Optimization: Foundations, Theory, and Methods
This tutorial presents the foundations, theory and methods of multiobjective
integer programming, with a particular focus on multi-objective combinatorial
optimization (MOCO). Many real-world optimization problems are inherently
combinatorial in nature and involve multiple, often conflicting, objectives. MOCO has
been widely used to model these complex decision problems across various domains
such as transportation, logistics, finance, energy, and healthcare. While the feasible
set is typically finite in MOCO problems, these solutions are not always explicitly
available to the decision-makers. Adding to this complexity, there is rarely a single
solution that optimizes all objectives simultaneously in multi-objective optimization
problems. This tutorial provides a structured framework for students, researchers, and
practitioners to approach and solve these complex decision problems. We first define
key terminology, describe the main characteristics of MOCO problems and discuss
their scalarization. We then explore the advanced methods and exact algorithms to
generate all nondominated points, for which an improvement in one objective cannot
be made without sacrificing performance in another. Since these algorithms become
intractable in real-world problem settings with the increase in the number of nondominated
points, we also discuss the methods that generate a representative set of
solutions with a prespecified level of quality or find preferred solutions. The tutorial
provides a broad and accessible overview of existing methods, supported by illustrative
examples, discussions, figures, and comprehensive references that clarify their
main ideas, strengths, and limitations.
Speaker: Banu Lokman
A Modern Treatment of the Primal–Dual Framework for Online Resource Allocation
Linear-programming (LP)-based primal–dual methods are fundamental for designing and analyzing algorithms in adversarial (prior-free) online resource allocation. This chapter provides a tutorial on two modern primal-dual frameworks, emphasizing recent developments and contemporary models in operations research. Part I develops an LP-based convex-programming framework where solving a regularized convex program at each arrival captures the tradeoff between greediness and hedging, yielding a dual certificate via Karush–Kuhn–Tucker (KKT) conditions. Because standard LP relaxations can be weak or intractable for stochastic outcomes, Part II introduces a complementary LP-free framework that provides a universal certificate system for evaluating competitive ratios under such uncertainty. Covering a wide array of models—including online vertex-weighted bipartite matching, edge-weighted online matching with free disposal, online matching with stochastic rewards, reusable resources, two-sided assortment optimization, configuration allocation (whole-page optimization), AdWords, and costly cancellations—the tutorial equips readers with versatile proof templates to analyze existing algorithms and develop new solutions for emerging applications.
Speakers: Rad Niazadeh, Rajan Udwani
Self-Adapting Approximations of Markov Decision Processes: A Guided Tour
Sequential decision making under uncertainty arises across business, engineering, and science. Markov Decision Processes (MDPs) offer a rich modeling language, but translating models into implementable policies requires confronting challenging state and action spaces and non-convex optimization landscapes. Approximations are essential, and making them accessible and performant without algorithmic expertise allows users to focus on formulating MDPs that capture real-world features rather than simplifying their models to facilitate solution. Obtaining a policy involves a three-stage COR cycle: Constructing a parametrized model that approximates the MDP, Optimizing for the parameters of this model, and Refining the model by learning from the
solution. These stages involve design choices that burden the user, leading them to simplify or skip stages.
This tutorial provides an overview of methods that reduce the user burden using COR as its guide. Construction ranges from lightweight extensible models to automated structural reformulations. Optimization leverages mathematical programming and firstorder methods that have matured in theory and off-the-shelf software. Refinement performs feature expansion and approximation tightening, feeding back into the construct stage. When a combination of techniques across COR stages results in both accessibility and performance, we refer to it as a self-adapting approximation. Such an approximation adapts to problem structure, instance data, or solution progress. We guide readers through these ideas across weakly coupled MDPs and general continuous state-action MDPs, providing generalizable foundations and a code base to get started on a simple example. The tutorial concludes by outlining the potential for foundation models and quantum computing to further impact this area.
Speakers: Andre Augusto Cire, Selvaprabu Nadarajah, Parshan Pakiman, Negar Soheili
A Tutorial on Reinforcement Learning for LLMs: RLHF and Beyond
coming soon
Speaker: Daniel Jiang
Foundations of Reinforcement Learning and Control: Connections and New Perspective
coming soon
Speakers: Claire Vernade, Onno Eberhard Max, Martha White, Florian Dörfler, Csaba Szepevari, Miroslav Krstic, Michael Muehlebach
Decision-Focused Learning: When and Why Traditional Prediction Models Fail
Plugging predictions of unknown parameters into downstream optimization
problems, often referred to as the “predict-then-optimize” paradigm, has long
been a standard approach in decision-making under uncertainty. However, improved
predictive accuracy does not, in general, translate into improved decision quality.
This disconnect has motivated growing interest in decision-focused learning (DFL)
within the operations research community. This tutorial reviews recent developments
in DFL and highlights key methodological insights, with a particular focus on stochastic
linear programming as the downstream decision-making problem.We discuss why
several widely used tools in traditional statistical learning are not directly suited to
decision-focused settings and must be rethought, including (i) data collection strategies
driven purely by predictive uncertainty and (ii) distributional distance measures
such as the Wasserstein distance. We summarize properties of DFL that distinguish it
from conventional predictive modeling and provide insights into the development of
new decision-focused tools.
Speaker: Mo Liu
Fraud Analytics as a Sequential Decision System: Integrating Machine Learning, Optimization, and Adversarial Learning
involving trade-offs between detection performance, investigation costs, and operational
constraints. While statistical and machine learning models are widely used to
detect anomalous behavior and estimate fraud risk, they are often deployed without
explicit consideration of downstream decisions, strategic adaptation, and system-level
dynamics. This tutorial presents a unified framework that reframes fraud analytics
as a sequential decision system involving adaptive and adversarial agents. We review
descriptive and predictive models, and embed them within a decision-theoretic framework
that captures trade-offs between false positives, false negatives, and resource
constraints. We further introduce adversarial risk analysis and related approaches to
model strategic interactions between fraudsters and detection systems. By connecting
prediction, optimization, and adversarial modeling, the tutorial highlights how decisions
influence both operational outcomes and future data through feedback effects.
This sequential perspective emphasizes the need for adaptive policies that account
for evolving fraud behavior and changing system conditions. Examples from health
care and financial fraud illustrate how analytical models support real-world decisionmaking
and resource allocation in high-stakes environments. Intended for researchers
and practitioners across operations research, statistics, and data science, this tutorial
provides an accessible synthesis that requires no prior background. By the end, the
reader will understand howto frame fraud detection as a decision problem, evaluate the
limitations of purely predictive approaches, and reason about adversarial adaptation
within a unified sequential framework applicable across fraud domains.
Speaker: Tahir Ekin
Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers
Artificial intelligence (AI) is moving beyond prediction toward systems
supporting decisions in complex, dynamic environments. This shift creates a natural
intersection with operations research and management science (OR/MS), which
has long provided methodological foundations for sequential decision making under
uncertainty. At the same time, deep learning advances, including feedforward neural
networks, recurrent architectures, transformers, large language models (LLMs),
and deep reinforcement learning, have expanded data-driven modeling for large-scale
decisions. This tutorial presents an OR/MS-centered perspective on deep learning
for sequential decision making under uncertainty, bridging neural architectures and
OR/MS approaches to decision making. Its premise: deep learning complements
optimization rather than replacing it. Deep learning brings adaptability and scalable
approximation, whereas OR/MS provides the mathematical rigor to represent constraints,
recourse, uncertainty, and decision quality. The tutorial reviews key decision
making foundations, connects them to the major neural architectures in modern AI, and
organizes the field around three central themes: predict-then-optimize and decisionaware
learning, learning-based decision generation under constraints for continuous
and discrete problems with temporal coupling, and deep reinforcement learning for
sequential and combinatorial decision making. Impact spans supply chains, service
systems, healthcare and epidemic response, agriculture, energy, environmental sustainability,
and autonomous operations. This tutorial frames these developments as
part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS’s
role in shaping the next generation of integrated learning–optimization systems.
Speaker: Esra Büyüktahtakın Toy
Multiagent Online Learning in Dynamic and Uncertain Environments
Speakers: Ceyhun Eksin, Jeff S. Shamma, Behrouz Touri
Parallel Computing for Two-Stage Stochastic Infrastructure Planning
Infrastructure planning has become increasingly difficult in recent years as natural hazards affect supply and demand patterns as well as the network of equipment connecting the two. In order to plan coordinated infrastructure systems that are resilient to a variety of potential threats, it is necessary to represent these systems at sufficiently high resolution to capture geographic and temporal variations as well as uncertainty. Both of these factors translate into much larger optimization problems than have traditionally been considered, and solving these problems is at the frontier of what is computationally feasible. Parallel computing is a tool to push that frontier.
In this tutorial, we present methods for solving large-scale two-stage stochastic
mixed-integer linear programming (MILP) problems using high-performance computing
(HPC) resources, with a focus on infrastructure planning problems. To this end,
we cover the necessary basics of modeling stochastic infrastructure planning problems
and leveraging parallel computing resources to solve stochastic MILPs. We discuss
decomposition algorithms and their parallel implementation in the Python package
mpi-sppy and present examples of how to use this tool to solve stochastic infrastructure
planning problems. Finally, we present an example of how mpi-sppy has
been used to solve a realistically sized power system expansion planning problem for
California to demonstrate the difficulty of solving large-scale, stochastic, infrastructure
planning problems and how HPC resources can be leveraged to solve such problems.
Speakers: Tomás Valencia Zuluaga, Elizabeth Glista, Amelia Musselman, and Jean-Paul Watson
GPU-Accelerated Decision Optimization
For decades, algorithms for solving decision optimization problems have been designed and implemented for CPUs. Recent advances in GPU hardware, driven by machine learning and AI, together with the development of GPU-accelerated scientificcomputing
kernels, have made GPUs a practical platform for solving optimization problems. This shift is most visible in linear programming, where first-order methods exploit GPU parallelism and high-bandwidth memory to solve problems with millions of variables and constraints. GPU algorithms for mixed-integer programming are still emerging, while GPU-based vehicle-routing
solvers are more mature and already support large-scale routing applications. At the same time, generative AI and agentic AI are changing how optimization models are formulated, solved, and embedded in decision workflows. This tutorial introduces GPU-accelerated decision optimization for researchers and practitioners familiar with CPU-based modeling and solvers.We review
computational patterns that make optimization algorithms amenable toGPUacceleration, summarize the growing ecosystem of opensource and commercial GPU solvers, and provide benchmarks that quantify current performance.We also present cuOpt, NVIDIA’s
open-source library for GPU-accelerated decision optimization. Our goal is to help the optimization community understand where GPUs are useful today, where important limitations remain, and where future research and development are needed.
Speakers: Nicolas Blin, Burcin Bozkaya, Akif Çördük, Chris Maes
