Related papers: Smooth Tchebycheff Scalarization for Multi-Objecti…
Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…
We describe a light-weight yet performant system for hyper-parameter optimization that approximately minimizes an overall scalar cost function that is obtained by combining multiple performance objectives using a target-priority-limit…
We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii)…
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained…
Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many…
Most multi-objective optimisation algorithms maintain an archive explicitly or implicitly during their search. Such an archive can be solely used to store high-quality solutions presented to the decision maker, but in many cases may…
Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex…
In this note we consider the iteration complexity of solving strongly convex multi objective optimization. We discuss the precise meaning of this problem, and indicate it is loosely defined, but the most natural notion is to find a set of…
Many machine learning tasks aim to find models that work well not for a single, but for a group of criteria, often opposing ones. One such example is imbalanced data classification, where, on the one hand, we want to achieve the best…
Real-world problems are often comprised of many objectives and require solutions that carefully trade-off between them. Current approaches to many-objective optimization often require challenging assumptions, like knowledge of the…
Many real-world applications involve black-box optimization of multiple objectives using continuous function approximations that trade-off accuracy and resource cost of evaluation. For example, in rocket launching research, we need to find…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
In this paper, we consider black-box multiobjective optimization problems in which all objective functions are not given analytically. In multiobjective optimization, it is important to produce a set of uniformly distributed discrete…
Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine…
We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function…
For the composite multi-objective optimization problem composed of two nonsmooth terms, a smoothing method is used to overcome the nonsmoothness of the objective function, making the objective function contain at most one nonsmooth term.…