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First-order methods (FOMs) have recently been applied and analyzed for solving problems with complicated functional constraints. Existing works show that FOMs for functional constrained problems have lower-order convergence rates than those…

This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…

We address the problem of characterizing $H$-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give several characterizations of a homomorphism dualities arising in a class of…

Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…

Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO…

The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the…

We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…

Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…

We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly…

Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…

Endogenous, i.e. decision-dependent, uncertainty has received increased interest in the stochastic programming community. In the robust optimization context, however, it has rarely been considered. This work addresses multistage robust…

Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…

Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…

This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

Robustness is often regarded as a critical future challenge for real-world applications, where stability is essential. However, as models often learn tasks in a similar order, we hypothesize that easier tasks will be easier regardless of…

Finding robust solutions of an optimization problem is an important issue in practice, and various concepts on how to define the robustness of a solution have been suggested. The idea of recoverable robustness requires that a solution can…

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…