Proyectos

Numerous real-life decision-making processes involve solving a task with uncertain input that can be estimated from historic data. There is a growing interest in decision-focused learning methods (a.k.a. smart predict-then-optimize) whose goal is to find models that fit the data while considering how the predicted input will perform in a particular task. For example, the task can be a shortest path problem that uses predictions on travel times in the objective function. Fitting the data and ignoring the task may lead to sub-optimal decisions. Sometimes, uncertainty is involved in the constraints of the model. In this case, ignoring the task would lead to infeasible decisions. The goal of this project is to develop efficient exact algorithms and new applications to train a Machine Learning models that perform well in one or several tasks using mathematical programming (MP) tools. In this context, the typical measure of a predictor is the regret: the excess cost incurred when making a suboptimal decision due to an imprecise predictor. This problem is bilevel in nature: the top-level decision consists in determining a predictor that minimizes a regret while considering that the predictions will affect a task, e.g. an optimization problem in a lower level. This structure is typically non-convex and non-continuous, making the problem difficult to solve for realistic instances. However, several recent advances in bilevel-tailored approaches exploit this structure and can solve large scale problems. There are two main ways of estimating task-oriented predictors: 1) stochastic gradient-based methods; and 2) MP reformulations of the problem. Stochastic gradient-based methods replace the non-differentiable regret for some differentiable surrogate loss function approximating the real loss. Due to advances in neural network implementations and stochastic gradient-descent this approach is the most applied among researchers and practitioners in the Machine Learning community. MP for data science has attracted the attention of researchers and practitioners in different areas as mathematics, operations research, computer science during the last years. It provides some degree of flexibility, being able to model desirable considerations for predictions models. For instance, MP has been successfully used to train sparse models yielding improved explainability and/or fairness. Moreover, MP models are in many cases solvable by any off-the-shelf solver. However, for the decision-focused learning problem there are still many gaps using MP formulations. To the best of our knowledge, MP formulations have been used only for surrogate loss functions. Behind the low usage of MP tools is the scalability. A typical ML setting involves data sets involving thousands of observations. In consequence, the training task becomes more difficult. To tackle this issue, decomposition methods such as cut and column generation can help to solve problems at scale. We aim to provide efficient exact methods that can return either optimal solutions, or optimality guarantees for large scale instances. During the last years, decision-focused learning has been widely applied to combinatorial optimization problems. However, this approach can also be used in many other applications such as Markov decision processes (MDPs) or game theory. In the first case, we can take algorithmic advantage of well-known existing algorithms for MDPs such as value iteration or policy iteration, or approximation techniques such as Q-learning. The game-theoretic setting is more challenging: depending on the notion of equilibrium the loss function would change. For instance, the definition of regret can be applied straightforwardly to Stackelberg equilibria (or leader-follower equilibria), a concept widely applied to energy markets, security and transportation. In the case of Nash equilibrium, the definition of regret is not direct anymore. We hope to develop models that adapt the decision-focused learning paradigm to this broader context. The study of this topic requires the use and development of MP of tools along with their algorithmic analysis. During the project, we expect to develop efficient of algorithms that can be used by decision making, as well as contribute in the understanding of the theoretical aspects of decision-focused learning.

La crisis hídrica provocada por el calentamiento global es uno de los problemas más importantes que afectan a regiones agrícolas como la sexta Región de O’Higgins. Este proyecto de vinculación internacional tiene como objetivo principal investigar distintos mecanismos para la asignación de recursos hídricos e épocas de escasez. En particular, se analizará el caso en que se tienen multiples usos de agua: distintos tipos de industrias (cupríferas y agrícola por ejemplo) y uso urbano. Este proyecto de vinculación internacional es liderado por el equipo nacional conformado por investigadores de la Universidad de O'Higgins y Universidad de Chile. Este proyecto incluye visitas del equipo nacional a los centros INRIA Sophia Antipolis, y INRAE en Montpellier, así como la organización de un workshop en la Universidad de O’Higgins.

Development of algorithms for bilevel optimization problems with applications in security, electricity and logistics.

El proyecto pretende desarrollar una herramienta que mejore la calidad de servicio en las rutas entregadas a los distintos clientes de Simpliroute, empresa nacional que entrega servicios de ruteo y recomendaciones de logística de última milla. Este desarrollo es en dos principales ámbitos. Primero, poder mejorar la capacidad de rutear a todos los clientes requeridos, detectando y anticipando con IA las ocasiones en donde el algoritmo de ruteo actual no encuentra una solución factible. El objetivo es detectar anticipadamente estos problemas de infactibilidad y proponer alternativas para entregar una mejor solución de ruteo. Segundo, usar la información de ajuste de rutas de los vehículos (detenciones, órdenes de visita, entre otros) para “aprender” de estos cambios usando IA, y mejorar la siguiente ruta a entregar. El prototipo a desarrollar se probará con las instancias de ruteo de diferentes clientes evaluando la calidad de servicio de la ruta y el reparto que realizan en sus operaciones.

El proyecto “Cambio climático y economía: análisis de riesgos y soluciones para sectores estratégicos” busca fortalecer las capacidades regionales de la Macrozona para enfrentar los crecientes desafíos del cambio climático mediante la creación de una red internacional de cooperación científica. La iniciativa se estructura en torno a tres ejes: la identificación y cuantificación de riesgos climáticos a nivel subregional, utilizando herramientas como imágenes satelitales, modelos de teoría de juegos y simulaciones; el análisis de cómo hogares, productores y gobiernos ajustan sus decisiones ; y el fortalecimiento de capacidades mediante pasantías internacionales, talleres, formación de estudiantes y la publicación de resultados. Un componente central del proyecto es el intercambio de experiencias entre países en desarrollo, México, Brasil y Chile, que comparten desafíos estructurales como alta informalidad laboral, barreras en el acceso al crédito y vulnerabilidad territorial frente al cambio climático. Además, el proyecto pone un fuerte énfasis en la formación de capital humano, incorporando a tesistas de pregrado y posgrado en todas las etapas de investigación. Ellas/os participarán en actividades clave como diseño de modelos, recolección y análisis de datos, y redacción de informes, fortaleciendo sus competencias técnicas y su vinculación con redes internacionales. Se ofrecerán también un workshop y un taller, orientado a fortalecer las capacidades en temas de economía del cambio climático. Participan la Universidad de O’Higgins y la Universidad de los Andes de Chile; y como socios internacionales el Banco Central de México y la Fundación Getulio Vargas de Brasil. Esta colaboración busca generar evidencia territorialmente situada para el diseño de planes de resiliencia agrícola, descentralizar la formación científica en Chile y consolidar una red duradera de investigación aplicada en economía del cambio climático con impacto regional y latinoamericano.

Postulación a Fondecyt Regular

Game theory and artificial intelligence are deeply connected fields, particularly when model- ing adversarial learning problems as Stackelberg games under uncertainty. In such settings, defenders allocate resources randomly to prevent attackers from anticipating their moves. As time evolves, the environment changes, and new strategies or actions may emerge. A suitable subfield of game theory to model these dynamics is stochastic games, where the state captures the set of available actions in a time-dependent process. Moreover, the attacker–defender inter- action naturally exhibits a hierarchical bilevel structure: the defender must design randomized strategies to protect targets, while the attacker responds by executing an action that maxi- mizes its reward. This makes stochastic dynamic Stackelberg games a model of choice for such applications [15], the Chilean party being very active in the domain [9, 10, 11]. In a previous collaboration [1], we have shown that defining an appropriate solution concept for these games is far from trivial, and in some cases remains an open research question. Even when a proper solution concept can be established, computing it becomes prohibitively expensive for games with massive state and action spaces. These challenges are not only of theoretical interest but also of high practical relevance. This associate team will focus on two among the many possible applications. Challenge 1: The first one is wildfire prevention. This theme has been widely examined in the literature, particularly through models that optimize the design of firebreaks [16], [12] and the the placement of surveillance cameras to limit fire spread. In contrast, the operational dimension of prevention and firefighting—where resources must be dynamically allocated un- der uncertainty—has received far less attention. Emerging distributed AI technologies with autonomous agents, both centralized (e.g., coordinated command-and-control systems) and de- centralized (e.g., drones and sensor swarms), could play a key role in addressing this challenge. Challenge 2: Similarly, in the domain of distributed AI learning systems (e.g. Federated Learning), a central authority is in charge of agregating the updates of distributed clients in the process of minimizing a global metric. The presence of Byzantine (or faulty) agents can derail convergence or induce a biais in this process. To mitigate this, robust agregation techniques have been proposed in the literature based on identifying and discarding suspect contributions [17, 18, 19]. But concrete attacks like ALIE [20] or FoE [21] tend to exhibit patterns. This lead researchers to propose the first history-aware defenses [22, 23, 24]. Purely deterministic rules, though, are likely to be defeated by powerful and well-informed agents. The attacker–defender framework is crucial to design secure training environments against adversarial manipulations, the principal issue being to decide if and when to exclude a suspected malicious agent. Both these applications can be tackeled with tools of Game Theory. More applications could be cited, like environmental conservation problems, such as poaching prevention [25], environmental tax evasion [26] or border patrol security [9].

El Centro de Modelamiento Matemático (CMM) es un centro científico líder en Chile para la investigación y aplicaciones de las matemáticas. Fue inaugurado en abril del 2000 y forma parte de la Facultad de Ciencias Físicas y Matemáticas (FCFM) de la Universidad de Chile, en la que se encuentra la principal y más antigua escuela de ingeniería del país. Su objetivo es crear nuevas matemáticas y utilizarlas para resolver problemas provenientes de otras ciencias, la industria y las políticas públicas.

En este proyecto, se busca general nuevas tecnologías que permitan mejorar el manejo de recursos hídricos en la sexta región. Director de línea "Gestión de Riego Intrapredial con Inteligencia Artificial"