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

We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…

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)…

We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\mathcal{O}(1/\sqrt{T})$…

To define a steepest descent method over a neural network, we need to choose a norm for each layer, a way to aggregate these norms across layers, and whether to use normalization. We systematically explore different alternatives for…

Most object detection methods operate by applying a binary classifier to sub-windows of an image, followed by a non-maximum suppression step where detections on overlapping sub-windows are removed. Since the number of possible sub-windows…

Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…

Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond…

When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence. In response to this challenge, we propose two types of the…

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve…

In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…

In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…

Multi-objective evolutionary algorithms (MOEAs) are essential for solving complex optimization problems, such as the diet problem, where balancing conflicting objectives, like cost and nutritional content, is crucial. However, most MOEAs…

Imaging in radioastronomy is an ill-posed inverse problem. Particularly the Event Horizon Telescope (EHT) Collaboration investigated the fidelity of their image reconstructions convincingly by large surveys solving the problem with…

Prior research on out-of-distribution detection (OoDD) has primarily focused on single-modality models. Recently, with the advent of large-scale pretrained vision-language models such as CLIP, OoDD methods utilizing such multi-modal…

The Word Movers Distance (WMD) measures the semantic dissimilarity between two text documents by computing the cost of optimally moving all words of a source/query document to the most similar words of a target document. Computing WMD…

In this work, the author presents a novel method for finding descent directions shared by two or more differentiable functions defined on the same unconstrained domain space. Then, the author illustrates an alternative Multiple-Gradient…

The principle of majorization-minimization (MM) provides a general framework for eliciting effective algorithms to solve optimization problems. However, they often suffer from slow convergence, especially in large-scale and high-dimensional…

Traditional multiobjective optimization problems (MOPs) are insufficiently equipped for scenarios involving multiple decision makers (DMs), which are prevalent in many practical applications. These scenarios are categorized as multiparty…

Given two point sets S and T, we study the many-to-many matching with demands problem (MMD problem) which is a generalization of the many-to-many matching problem (MM problem). In an MMD, each point of one set must be matched to a given…