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We study the unbalanced optimal transport (UOT) problem, where the marginal constraints are enforced using Maximum Mean Discrepancy (MMD) regularization. Our work is motivated by the observation that the literature on UOT is focused on regularization based on $\phi$-divergence (e.g., KL divergence). Despite the popularity of MMD, its role as a regularizer in the context of UOT seems less understood. We begin by deriving a specific dual of MMD-regularized UOT (MMD-UOT), which helps us prove several useful properties. One interesting outcome of this duality result is that MMD-UOT induces novel metrics, which not only lift the ground metric like the Wasserstein but are also sample-wise efficient to estimate like the MMD. Further, for real-world applications involving non-discrete measures, we present an estimator for the transport plan that is supported only on the given ($m$) samples. Under certain conditions, we prove that the estimation error with this finitely-supported transport plan is also $\mathcal{O}(1/\sqrt{m})$. As far as we know, such error bounds that are free from the curse of dimensionality are not known for $\phi$-divergence regularized UOT. Finally, we discuss how the proposed estimator can be computed efficiently using accelerated gradient descent. Our experiments show that MMD-UOT consistently outperforms popular baselines, including KL-regularized UOT and MMD, in diverse machine learning applications. Our codes are publicly available at //github.com/Piyushi-0/MMD-reg-OT

We consider the problem of policy transfer between two Markov Decision Processes (MDPs). We introduce a lemma based on existing theoretical results in reinforcement learning to measure the relativity gap between two arbitrary MDPs, that is the difference between any two cumulative expected returns defined on different policies and environment dynamics. Based on this lemma, we propose two new algorithms referred to as Relative Policy Optimization (RPO) and Relative Transition Optimization (RTO), which offer fast policy transfer and dynamics modelling, respectively. RPO transfers the policy evaluated in one environment to maximize the return in another, while RTO updates the parameterized dynamics model to reduce the gap between the dynamics of the two environments. Integrating the two algorithms results in the complete Relative Policy-Transition Optimization (RPTO) algorithm, in which the policy interacts with the two environments simultaneously, such that data collections from two environments, policy and transition updates are completed in one closed loop to form a principled learning framework for policy transfer. We demonstrate the effectiveness of RPTO on a set of MuJoCo continuous control tasks by creating policy transfer problems via variant dynamics.

We consider the movable antenna (MA) array-enabled wireless communication with coordinate multi-point (CoMP) reception, where multiple destinations adopt the maximal ratio combination technique to jointly decode the common message sent from the transmitter equipped with the MA array. Our goal is to maximize the effective received signal-to-noise ratio, by jointly optimizing the transmit beamforming and the positions of the MA array. Although the formulated problem is highly non-convex, we reveal that it is fundamental to maximize the principal eigenvalue of a hermite channel matrix which is a function of the positions of the MA array. The corresponding sub-problem is still non-convex, for which we develop a computationally efficient algorithm. Afterwards, the optimal transmit beamforming is determined with a closed-form solution. In addition, the theoretical performance upper bound is analyzed. Since the MA array brings an additional spatial degree of freedom by flexibly adjusting all antennas' positions, it achieves significant performance gain compared to competitive benchmarks.

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational complexity, and the solutions are very noise-sensitive. We generalize a multiscale spatial regularization approach to solve the unmixing problem by incorporating group sparsity-inducing mixed norms. Then, we propose a noise-robust method that can take advantage of the bundle structure to deal with endmember variability while ensuring inter- and intra-class sparsity in abundance estimation with reasonable computational cost. We also present a general heuristic to select the \emph{most representative} abundance estimation over multiple runs of the unmixing process, yielding a solution that is robust and highly reproducible. Experiments illustrate the robustness and consistency of the results when compared to related methods.

We consider the fundamental task of network exploration. A network is modeled as a simple connected undirected n-node graph with unlabeled nodes, and all ports at any node of degree d are arbitrarily numbered 0,.....,d-1. Each of two identical mobile agents, initially situated at distinct nodes, has to visit all nodes and stop. Agents execute the same deterministic algorithm and move in synchronous rounds: in each round, an agent can either remain at the same node or move to an adjacent node. Exploration must be collision-free: in every round at most one agent can be at any node. We assume that agents have vision of radius 2: an awake agent situated at a node v can see the subgraph induced by all nodes at a distance at most 2 from v, sees all port numbers in this subgraph, and the agents located at these nodes. Agents do not know the entire graph but they know an upper bound n on its size. The time of an exploration is the number of rounds since the wakeup of the later agent to the termination by both agents. We show a collision-free exploration algorithm working in time polynomial in n, for arbitrary graphs of size larger than 2. Moreover, we show that if agents have only vision of radius 1, then collision-free exploration is impossible, e.g., in any tree of diameter 2.

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.

Deep neural networks have shown remarkable performance in image classification. However, their performance significantly deteriorates with corrupted input data. Domain generalization methods have been proposed to train robust models against out-of-distribution data. Data augmentation in the frequency domain is one of such approaches that enable a model to learn phase features to establish domain-invariant representations. This approach changes the amplitudes of the input data while preserving the phases. However, using fixed phases leads to susceptibility to phase fluctuations because amplitudes and phase fluctuations commonly occur in out-of-distribution. In this study, to address this problem, we introduce an approach using finite variation of the phases of input data rather than maintaining fixed phases. Based on the assumption that the degree of domain-invariant features varies for each phase, we propose a method to distinguish phases based on this degree. In addition, we propose a method called vital phase augmentation (VIPAug) that applies the variation to the phases differently according to the degree of domain-invariant features of given phases. The model depends more on the vital phases that contain more domain-invariant features for attaining robustness to amplitude and phase fluctuations. We present experimental evaluations of our proposed approach, which exhibited improved performance for both clean and corrupted data. VIPAug achieved SOTA performance on the benchmark CIFAR-10 and CIFAR-100 datasets, as well as near-SOTA performance on the ImageNet-100 and ImageNet datasets. Our code is available at //github.com/excitedkid/vipaug.

This paper considers the optimal sensor allocation for estimating the emission rates of multiple sources in a two-dimensional spatial domain. Locations of potential emission sources are known (e.g., factory stacks), and the number of sources is much greater than the number of sensors that can be deployed, giving rise to the optimal sensor allocation problem. In particular, we consider linear dispersion forward models, and the optimal sensor allocation is formulated as a bilevel optimization problem. The outer problem determines the optimal sensor locations by minimizing the overall Mean Squared Error of the estimated emission rates over various wind conditions, while the inner problem solves an inverse problem that estimates the emission rates. Two algorithms, including the repeated Sample Average Approximation and the Stochastic Gradient Descent based bilevel approximation, are investigated in solving the sensor allocation problem. Convergence analysis is performed to obtain the performance guarantee, and numerical examples are presented to illustrate the proposed approach.

The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. In addition, Binary Cross Entropy (BCE) loss, which shows conspicuous performance with ViTs, encounters predicaments in LTR. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins to deploy it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves 81.0% Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at //github.com/XuZhengzhuo/LiVT.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.