Related papers: Two-Stage Predict+Optimize for Mixed Integer Linea…
Algorithms with predictions} has emerged as a powerful framework to combine the robustness of traditional online algorithms with the data-driven performance benefits of machine-learned (ML) predictions. However, most existing approaches in…
This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…
This paper presents a novel hybrid approach that integrates linear programming (LP) within the loss function of an unsupervised machine learning model. By leveraging the strengths of both optimization techniques and machine learning, this…
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…
Contextual optimization, also known as predict-then-optimize or prescriptive analytics, considers an optimization problem with the presence of covariates (context or side information). The goal is to learn a prediction model (from the…
We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by…
Although energy system optimisation based on linear optimisation is often used for influential energy outlooks and studies for political decision-makers, the underlying background still needs to be described in the scientific literature in…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes.…
We consider the problem of learning fair policies for multi-stage selection problems from observational data. This problem arises in several high-stakes domains such as company hiring, loan approval, or bail decisions where outcomes (e.g.,…
In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define…
In this paper, we study the predict-then-optimize problem where the output of a machine learning prediction task is used as the input of some downstream optimization problem, say, the objective coefficient vector of a linear program. The…
We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework,…