Although previous graph-based multi-view clustering algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view-consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the k-means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this paper presents an efficient multi-view clustering approach via unified and discrete bipartite graph learning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view-consensus bipartite graph with adaptive weight learning. Further, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view-consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.

We study the problem of zeroth-order (black-box) optimization of a Lipschitz function $f$ defined on a compact subset $\mathcal X$ of $\mathbb R^d$, with the additional constraint that algorithms must certify the accuracy of their recommendations. We characterize the optimal number of evaluations of any Lipschitz function $f$ to find and certify an approximate maximizer of $f$ at accuracy $\varepsilon$. Under a weak assumption on $\mathcal X$, this optimal sample complexity is shown to be nearly proportional to the integral $\int_{\mathcal X} \mathrm{d}\boldsymbol x/( \max(f) - f(\boldsymbol x) + \varepsilon )^d$. This result, which was only (and partially) known in dimension $d=1$, solves an open problem dating back to 1991. In terms of techniques, our upper bound relies on a packing bound by Bouttier al. (2020) for the Piyavskii-Shubert algorithm that we link to the above integral. We also show that a certified version of the computationally tractable DOO algorithm matches these packing and integral bounds. Our instance-dependent lower bound differs from traditional worst-case lower bounds in the Lipschitz setting and relies on a local worst-case analysis that could likely prove useful for other learning tasks.

Federated Learning (FL) can be used in mobile edge networks to train machine learning models in a distributed manner. Recently, FL has been interpreted within a Model-Agnostic Meta-Learning (MAML) framework, which brings FL significant advantages in fast adaptation and convergence over heterogeneous datasets. However, existing research simply combines MAML and FL without explicitly addressing how much benefit MAML brings to FL and how to maximize such benefit over mobile edge networks. In this paper, we quantify the benefit from two aspects: optimizing FL hyperparameters (i.e., sampled data size and the number of communication rounds) and resource allocation (i.e., transmit power) in mobile edge networks. Specifically, we formulate the MAML-based FL design as an overall learning time minimization problem, under the constraints of model accuracy and energy consumption. Facilitated by the convergence analysis of MAML-based FL, we decompose the formulated problem and then solve it using analytical solutions and the coordinate descent method. With the obtained FL hyperparameters and resource allocation, we design a MAML-based FL algorithm, called Automated Federated Learning (AutoFL), that is able to conduct fast adaptation and convergence. Extensive experimental results verify that AutoFL outperforms other benchmark algorithms regarding the learning time and convergence performance.

In this work we present an "out-of-the-box" application of Machine Learning (ML) optimizers for an industrial optimization problem. We introduce a piecewise polynomial model (spline) for fitting of $\mathcal{C}^k$-continuos functions, which can be deployed in a cam approximation setting. We then use the gradient descent optimization context provided by the machine learning framework TensorFlow to optimize the model parameters with respect to approximation quality and $\mathcal{C}^k$-continuity and evaluate available optimizers. Our experiments show that the problem solution is feasible using TensorFlow gradient tapes and that AMSGrad and SGD show the best results among available TensorFlow optimizers. Furthermore, we introduce a novel regularization approach to improve SGD convergence. Although experiments show that remaining discontinuities after optimization are small, we can eliminate these errors using a presented algorithm which has impact only on affected derivatives in the local spline segment.

Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations. These relaxations are solved with a Frank-Wolfe algorithm over the convex hull of mixed-integer feasible points instead of the continuous relaxation via calls to a mixed-integer linear solver as the linear oracle. The proposed method computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of mixed-integer linear solvers without an outer approximation scheme and can exploit inexact solutions of node subproblems.

Cloud Robotics is helping to create a new generation of robots that leverage the nearly unlimited resources of large data centers (i.e., the cloud), overcoming the limitations imposed by on-board resources. Different processing power, capabilities, resource sizes, energy consumption, and so forth, make scheduling and task allocation critical components. The basic idea of task allocation and scheduling is to optimize performance by minimizing completion time, energy consumption, delays between two consecutive tasks, along with others, and maximizing resource utilization, number of completed tasks in a given time interval, and suchlike. In the past, several works have addressed various aspects of task allocation and scheduling. In this paper, we provide a comprehensive overview of task allocation and scheduling strategies and related metrics suitable for robotic network cloud systems. We discuss the issues related to allocation and scheduling methods and the limitations that need to be overcome. The literature review is organized according to three different viewpoints: Architectures and Applications, Methods and Parameters. In addition, the limitations of each method are highlighted for future research.

Recently, evolutionary computation (EC) has been promoted by machine learning, distributed computing, and big data technologies, resulting in new research directions of EC like distributed EC and surrogate-assisted EC. These advances have significantly improved the performance and the application scope of EC, but also trigger privacy leakages, such as the leakage of optimal results and surrogate model. Accordingly, evolutionary computation combined with privacy protection is becoming an emerging topic. However, privacy concerns in evolutionary computation lack a systematic exploration, especially for the object, motivation, position, and method of privacy protection. To this end, in this paper, we discuss three typical optimization paradigms (i.e., \textit{centralized optimization, distributed optimization, and data-driven optimization}) to characterize optimization modes of evolutionary computation and propose BOOM to sort out privacy concerns in evolutionary computation. Specifically, the centralized optimization paradigm allows clients to outsource optimization problems to the centralized server and obtain optimization solutions from the server. While the distributed optimization paradigm exploits the storage and computational power of distributed devices to solve optimization problems. Also, the data-driven optimization paradigm utilizes data collected in history to tackle optimization problems lacking explicit objective functions. Particularly, this paper adopts BOOM to characterize the object and motivation of privacy protection in three typical optimization paradigms and discusses potential privacy-preserving technologies balancing optimization performance and privacy guarantees in three typical optimization paradigms. Furthermore, this paper attempts to foresee some new research directions of privacy-preserving evolutionary computation.

We study routing for on-demand last-mile logistics with two crucial novel features: i) Multiple depots, optimizing where to pick-up every order, ii) Allowing vehicles to perform depot returns prior to being empty, thus adapting their routes to include new orders online. Both features result in shorter distances and more agile planning. We propose a scalable dynamic method to deliver orders as fast as possible. Following a rolling horizon approach, each time step the following is executed. First, define potential pick-up locations and identify which groups of orders can be transported together, with which vehicle and following which route. Then, decide which of these potential groups of orders will be executed and by which vehicle by solving an integer linear program. We simulate one day of service in Amsterdam that considers 10,000 requests, compare results to several strategies and test different scenarios. Results underpin the advantages of the proposed method

We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that minimizes the sum of entropic optimal transport (EOT) costs with respect to a family of given probability measures, plus an entropy term. We denote it $(\lambda,\tau)$-barycenter, where $\lambda$ is the inner regularization strength and $\tau$ the outer one. This formulation recovers several previously proposed EOT barycenters for various choices of $\lambda,\tau \geq 0$ and generalizes them. First, in spite of -- and in fact owing to -- being \emph{doubly} regularized, we show that our formulation is debiased for $\tau=\lambda/2$: the suboptimality in the (unregularized) Wasserstein barycenter objective is, for smooth densities, of the order of the strength $\lambda^2$ of entropic regularization, instead of $\max\{\lambda,\tau\}$ in general. We discuss this phenomenon for isotropic Gaussians where all $(\lambda,\tau)$-barycenters have closed form. Second, we show that for $\lambda,\tau>0$, this barycenter has a smooth density and is strongly stable under perturbation of the marginals. In particular, it can be estimated efficiently: given $n$ samples from each of the probability measures, it converges in relative entropy to the population barycenter at a rate $n^{-1/2}$. And finally, this formulation lends itself naturally to a grid-free optimization algorithm: we propose a simple \emph{noisy particle gradient descent} which, in the mean-field limit, converges globally at an exponential rate to the barycenter.

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.