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Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the…
Hard optimisation problems such as Boolean Satisfiability typically have long solving times and can usually be solved by many algorithms, although the performance can vary widely in practice. Research has shown that no single algorithm…
Many real-world problems require trading off multiple competing objectives. However, these objectives are often in different units and/or scales, which can make it challenging for practitioners to express numerical preferences over…
We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…
In fields such as medicine and drug discovery, the ultimate goal of a classification is not to guess a class, but to choose the optimal course of action among a set of possible ones, usually not in one-one correspondence with the set of…
While reinforcement learning algorithms provide automated acquisition of optimal policies, practical application of such methods requires a number of design decisions, such as manually designing reward functions that not only define the…
Simulation is a useful tool in situations where training data for machine learning models is costly to annotate or even hard to acquire. In this work, we propose a reinforcement learning-based method for automatically adjusting the…
We consider the problem of learning a loss function which, when minimized over a training dataset, yields a model that approximately minimizes a validation error metric. Though learning an optimal loss function is NP-hard, we present an…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…
A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an ``optimal'' predicted outcome distribution according to some…
Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance…
We study multi-objective reinforcement learning with nonlinear preferences over trajectories. That is, we maximize the expected value of a nonlinear function over accumulated rewards (expected scalarized return or ESR) in a multi-objective…