Combinatorial optimization (CO) is a fundamental tool in many fields. Many neural combinatorial optimization (NCO) methods have been proposed to solve CO problems. However, existing NCO methods typically require significant computational and storage resources, and face challenges in maintaining robustness to distribution shifts between training and test data. To address these issues, we model CO instances into probability measures, and introduce Wasserstein-based metrics to quantify the difference between CO instances. We then leverage a popular data compression technique, \emph{coreset}, to construct a small-size proxy for the original large dataset. However, the time complexity of constructing a coreset is linearly dependent on the size of the dataset. Consequently, it becomes challenging when datasets are particularly large. Further, we accelerate the coreset construction by adapting it to the merge-and-reduce framework, enabling parallel computing. Additionally, we prove that our coreset is a good representation in theory. {Subsequently}, to speed up the training process for existing NCO methods, we propose an efficient training framework based on the coreset technique. We train the model on a small-size coreset rather than on the full dataset, and thus save substantial computational and storage resources. Inspired by hierarchical Gonzalez’s algorithm, our coreset method is designed to capture the diversity of the dataset, which consequently improves robustness to distribution shifts. Finally, experimental results demonstrate that our training framework not only enhances robustness to distribution shifts but also achieves better performance with reduced resource requirements.

Conditional Generative Adversarial Network (cGAN) is an important type of GAN which is often equipped with an auxiliary classifier. However, existing cGANs usually have the issue of mode collapse which can incur unstable performance in practice. In this paper, we propose a novel stable training method for cGANs with well preserving the generation fidelity and diversity. Our key ideas are designing efficient adversarial training strategies for the auxiliary classifier and mitigating the overconfidence issue caused by the cross-entropy loss. We propose a classifier-based cGAN called Confidence Guided Generative Adversarial Networks (CG-GAN) by introducing the adversarial training to a K-way classifier. In particular, we show in theory that the obtained K-way classifier can encourage the generator to learn the real joint distribution. To further enhance the performance and stability, we propose to establish a high-entropy prior label distribution for the generated data and incorporate a reverse KL divergence term into the minimax loss of CG-GAN. Through a comprehensive set of experiments on the popular benchmark datasets, including the large-scale dataset ImageNet, we demonstrate the advantages of our proposed method over several state-of-the-art cGANs.

Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \textsf{WDRO} can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast \textsf{WDRO} training algorithms for some specific machine learning tasks (e.g., logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale \textsf{WDRO}s is still quite limited, to the best of our knowledge. \textit{Coreset} is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the $\epsilon$-coreset for the general \textsf{WDRO} problems. Though it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \textsf{WDRO}. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original \textsf{WDRO} objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of \textsf{WDRO}. Finally, we implement our coreset approach and illustrate its effectiveness for several \textsf{WDRO} problems in the experiments. See \href{https://arxiv.org/abs/2210.04260}{arXiv:2210.04260} for the full version of this paper. The code is available at \url{https://github.com/h305142/WDRO_coreset}.

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational complexity. Coreset is a popular data compression technique that has been extensively studied before. However, most of existing coreset methods are problem-dependent and cannot be used as a general tool for a broader range of applications. A key obstacle is that they often rely on the pseudo-dimension and total sensitivity bound that can be very high or hard to obtain. In this paper, based on the “locality” property of gradient descent algorithms, we propose a new framework, termed “sequential coreset”, which effectively avoids these obstacles. Moreover, our method is particularly suitable for sparse optimization whence the coreset size can be further reduced to be only poly-logarithmically dependent on the dimension. In practice, the experimental results suggest that our method can save a large amount of running time compared with the baseline algorithms.

Some real-world optimization problems involve multiple decision makers holding different positions, each of whom has multiple conflicting objectives. These problems are defined as multiparty multiobjective optimization problems (MPMOPs). Although evolutionary multiobjective optimization has been widely studied for many years, little attention has been paid to multiparty multiobjective optimization in the field of evolutionary computation. In this paper, a class of MPMOPs, that is, MPMOPs having common Pareto optimal solutions, is addressed. A benchmark for MPMOPs, obtained by modifying an existing dynamic multiobjective optimization benchmark, is provided, and a multiparty multiobjective evolutionary algorithm to find the common Pareto optimal set is proposed. The results of experiments conducted using the benchmark show that the proposed multiparty multiobjective evolutionary algorithm is effective.