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We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…

Many practical optimization problems involve uncertain parameters that are strictly positive. However, the most common uncertainty sets used in robust optimization are the box and the ellipsoidal sets, which may include non-positive values…

We present a fully probabilistic approach for solving binary optimization problems with black-box objective functions and with budget constraints. In the probabilistic approach, the optimization variable is viewed as a random variable and…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Uncertainty sampling is a prevalent active learning algorithm that queries sequentially the annotations of data samples which the current prediction model is uncertain about. However, the usage of uncertainty sampling has been largely…

This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

Constrained multiobjective optimization has gained much interest in the past few years. However, constrained multiobjective optimization problems (CMOPs) are still unsatisfactorily understood. Consequently, the choice of adequate CMOPs for…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Ensuring fairness in computational problems has emerged as a $key$ topic during recent years, buoyed by considerations for equitable resource distributions and social justice. It $is$ possible to incorporate fairness in computational…

This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…

The difficulty of solving a multi-objective optimization problem is impacted by the number of objectives to be optimized. The presence of many objectives typically introduces a number of challenges that affect the choice/design of…

Benchmarks are a useful tool for empirical performance comparisons. However, one of the main shortcomings of existing benchmarks is that it remains largely unclear how they relate to real-world problems. What does an algorithm's performance…

Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic…

Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be…

The necessity to deal with uncertain data is a major challenge in decision making. Robust optimization emerged as one of the predominant paradigms to produce solutions that hedge against uncertainty. In order to obtain an even more…

Unquantified sources of uncertainty in observational causal analyses can break the integrity of the results. One would never want another analyst to repeat a calculation with the same dataset, using a seemingly identical procedure, only to…