Related papers: An Extension of the Non-Inferior Set Estimation Al…
Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…
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…
In decision-making systems, algorithmic recourse aims to identify minimal-cost actions to alter an individual features, thereby obtaining a desired outcome. This empowers individuals to understand, question, or alter decisions that…
We present an algorithm for multi-objective optimization of computationally expensive problems. The proposed algorithm is based on solving a set of surrogate problems defined by models of the real one, so that only solutions estimated to be…
This work aims at developing new methodologies to optimize computational costly complex systems (e.g., aeronautical engineering systems). The proposed surrogate-based method (often called Bayesian optimization) uses adaptive sampling to…
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…
This paper studies an entropy-based multi-objective Bayesian optimization (MBO). The entropy search is successful approach to Bayesian optimization. However, for MBO, existing entropy-based methods ignore trade-off among objectives or…
Multi-agent optimization problems with many objective functions have drawn much interest over the past two decades. Many works on the subject minimize the sum of objective functions, which implicitly carries a decision about the problem…
Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…
Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
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…
A key task in multi-objective optimization is to compute the Pareto subset or frontier $P$ of a given $d$-dimensional objective space $F$; that is, a maximal subset $P\subseteq F$ such that every element in $P$ is not-dominated (it is not…
In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs.…
Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver NExOS…
We consider the problem of active learning in the context of spatial sampling for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible.…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
Query plans are compared according to multiple cost metrics in multi-objective query optimization. The goal is to find the set of Pareto plans realizing optimal cost tradeoffs for a given query. So far, only algorithms with exponential…