相关论文: MMD-Newton Method for Multi-objective Optimization

We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…

Bayesian Neural Networks (BNNs) are trained to optimize an entire distribution over their weights instead of a single set, having significant advantages in terms of, e.g., interpretability, multi-task learning, and calibration. Because of…

Given two point sets $S$ and $T$, the minimum-cost many-to-many matching with demands (MMD) problem is the problem of finding a minimum-cost many-to-many matching between $S$ and $T$ such that each point of $S$ (respectively $T$) is matched…

Multi-objective optimization (MOO) has become an influential framework in many machine learning problems with multiple objectives such as learning with multiple criteria and multi-task learning (MTL). In this paper, we propose a new…

Most multimodal multi-objective evolutionary algorithms (MMEAs) aim to find all global Pareto optimal sets (PSs) for a multimodal multi-objective optimization problem (MMOP). However, in real-world problems, decision makers (DMs) may be…

Recently, there has been an increasing interest in the application of multiobjective optimization (MOO) in machine learning (ML). This interest is driven by the numerous real-life situations where multiple objectives must be optimized…

In this paper, multi-snapshot Newtonized orthogonal matching pursuit (MNOMP) algorithm is proposed to deal with the line spectrum estimation with multiple measurement vectors (MMVs). MNOMP has the low computation complexity and…

The imbalances and conditioning of the objective functions influence the performance of first-order methods for multiobjective optimization problems (MOPs). The latter is related to the metric selected in the direction-finding subproblems.…

This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…

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…

Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric…

The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be found, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for…

Multi-objective optimization (MOO) is receiving more attention in various fields such as multi-task learning. Recent works provide some effective algorithms with theoretical analysis but they are limited by the standard $L$-smooth or…

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…

Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD),…

Modern machine learning models are often constructed taking into account multiple objectives, e.g., minimizing inference time while also maximizing accuracy. Multi-objective hyperparameter optimization (MHPO) algorithms return such…

The major difficulty in Multi-objective Optimization Evolutionary Algorithms (MOEAs) is how to find an appropriate solution that is able to converge towards the true Pareto Front with high diversity. Most existing methodologies, which have…

Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures…

The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able…

The multi-gradient descent algorithm (MGDA) finds a common descent direction that can improve all objectives by identifying the minimum-norm point in the convex hull of the objective gradients. This method has become a foundational tool in…