As a widely observable social effect, influence diffusion refers to a process where innovations, trends, awareness, etc. spread across the network via the social impact among individuals. Motivated by such social effect, the concept of influence maximization is coined, where the goal is to select a bounded number of the most influential nodes (seed nodes) from a social network so that they can jointly trigger the maximal influence diffusion. A rich body of research in this area is performed under statistical diffusion models with provable submodularity, which essentially simplifies the problem as the optimal result can be approximated by the simple greedy search. When the diffusion models are non-submodular, however, the research community mostly focuses on how to bound/approximate them by tractable submodular functions so as to estimate the optimal result. In other words, there is still a lack of efficient methods that can directly resolve non-submodular influence maximization problems. In this regard, we fill the gap by proposing seed selection strategies using network graphical properties in a generalized threshold-based model, called influence barricade model, which is non-submodular. Specifically, under this model, we first establish theories to reveal graphical conditions that ensure the network generated by node removals has the same optimal seed set as that in the original network. We then exploit these theoretical conditions to develop efficient algorithms by strategically removing less-important nodes and selecting seeds only in the remaining network. To the best of our knowledge, this is the first graph-based approach that directly tackles non-submodular influence maximization.

Belief propagation is an algorithm that is known from statistical physics and computer science. It provides an efficient way of calculating marginals that involve large sums of products which are efficiently rearranged into nested products of sums to approximate the marginals. It allows a reliable estimation of the state and its variance of power grids that is needed for the control and forecast of power grid management. At prototypical examples of IEEE-grids we show that belief propagation not only scales linearly with the grid size for the state estimation itself, but also facilitates and accelerates the retrieval of missing data and allows an optimized positioning of measurement units. Based on belief propagation, we give a criterion for how to assess whether other algorithms, using only local information, are adequate for state estimation for a given grid. We also demonstrate how belief propagation can be utilized for coarse-graining power grids towards representations that reduce the computational effort when the coarse-grained version is integrated into a larger grid. It provides a criterion for partitioning power grids into areas in order to minimize the error of flow estimates between different areas.

In this paper, we investigate an important research question in the car sequencing problem, that is, what characteristics make an instance hard to solve? To do so, we carry out an Instance Space Analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance and projecting feature vectors onto a two-dimensional space using principal component analysis. The resulting two dimensional visualizations provide insights into both the characteristics of the instances used for testing and to compare how these affect different optimisation algorithms. This guides us in constructing a new set of benchmark instances with a range of instance properties. These are shown to be both more diverse than the previous benchmarks and include many hard to solve instances. We systematically compare the performance of six algorithms for solving the car sequencing problem. The methods tested include three existing algorithms from the literature and three new ones. Importantly, we build machine learning models to identify the niche in the instance space that an algorithm is expected to perform well on. Our results show that the new algorithms are state-of-the-art. This analysis helps to understand problem hardness and select an appropriate algorithm for solving a given car sequencing problem instance.

Bayesian optimisation presents a sample-efficient methodology for global optimisation. Within this framework, a crucial performance-determining subroutine is the maximisation of the acquisition function, a task complicated by the fact that acquisition functions tend to be non-convex and thus nontrivial to optimise. In this paper, we undertake a comprehensive empirical study of approaches to maximise the acquisition function. Additionally, by deriving novel, yet mathematically equivalent, compositional forms for popular acquisition functions, we recast the maximisation task as a compositional optimisation problem, allowing us to benefit from the extensive literature in this field. We highlight the empirical advantages of the compositional approach to acquisition function maximisation across 3958 individual experiments comprising synthetic optimisation tasks as well as tasks from Bayesmark. Given the generality of the acquisition function maximisation subroutine, we posit that the adoption of compositional optimisers has the potential to yield performance improvements across all domains in which Bayesian optimisation is currently being applied.

We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one projections of an approximately low-rank PSD matrix, we characterize the radius of the set of PSD matrices that satisfy the measurements. This result yields a sampling rate to guarantee singleton solution sets when the true matrix is exactly low-rank, such that the choice of the objective function or the algorithm to be used is inconsequential in its recovery. We discuss applications of this contribution and compare it to recent literature regarding implicit regularization for similar problems. We demonstrate practical implications of this result by applying conic projection methods for PSD matrix recovery without incorporating low-rank regularization.

Applications such as simulating large quantum systems or solving large-scale linear algebra problems are immensely challenging for classical computers due their extremely high computational cost. Quantum computers promise to unlock these applications, although fault-tolerant quantum computers will likely not be available for several years. Currently available quantum devices have serious constraints, including limited qubit numbers and noise processes that limit circuit depth. Variational Quantum Algorithms (VQAs), which employ a classical optimizer to train a parametrized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisioned for quantum computers, and they appear to the best hope for obtaining quantum advantage. Nevertheless, challenges remain including the trainability, accuracy, and efficiency of VQAs. In this review article we present an overview of the field of VQAs. Furthermore, we discuss strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage.

This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a co-association matrix, which indicates the pairwise similarity between samples, as the weighted linear combination of the connective matrices from different base clusterings, and the resulting co-association matrix is then adopted as the input of an off-the-shelf clustering algorithm, e.g., spectral clustering. However, the co-association matrix may be dominated by poor base clusterings, resulting in inferior performance. In this paper, we propose a novel low-rank tensor approximation-based method to solve the problem from a global perspective. Specifically, by inspecting whether two samples are clustered to an identical cluster under different base clusterings, we derive a coherent-link matrix, which contains limited but highly reliable relationships between samples. We then stack the coherent-link matrix and the co-association matrix to form a three-dimensional tensor, the low-rankness property of which is further explored to propagate the information of the coherent-link matrix to the co-association matrix, producing a refined co-association matrix. We formulate the proposed method as a convex constrained optimization problem and solve it efficiently. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods. To the best of our knowledge, this is the first work to explore the potential of low-rank tensor on clustering ensemble, which is fundamentally different from previous approaches.

In this short note, we describe our submission to the NeurIPS 2020 BBO challenge. Motivated by the fact that different optimizers work well on different problems, our approach switches between different optimizers. Since the team names on the competition's leaderboard were randomly generated "alliteration nicknames", consisting of an adjective and an animal with the same initial letter, we called our approach the Switching Squirrel, or here, short, Squirrel. The challenge mandated to suggest 16 successive batches of 8 hyperparameter configurations at a time. We chose to only use one optimizer for a given batch, warmstarted with all previous observations.

Traditional optimization algorithms search for a single global optimum that maximizes (or minimizes) the objective function. Multimodal optimization algorithms search for the highest peaks in the search space that can be more than one. Quality-Diversity algorithms are a recent addition to the evolutionary computation toolbox that do not only search for a single set of local optima, but instead try to illuminate the search space. In effect, they provide a holistic view of how high-performing solutions are distributed throughout a search space. The main differences with multimodal optimization algorithms are that (1) Quality-Diversity typically works in the behavioral space (or feature space), and not in the genotypic (or parameter) space, and (2) Quality-Diversity attempts to fill the whole behavior space, even if the niche is not a peak in the fitness landscape. In this chapter, we provide a gentle introduction to Quality-Diversity optimization, discuss the main representative algorithms, and the main current topics under consideration in the community. Throughout the chapter, we also discuss several successful applications of Quality-Diversity algorithms, including deep learning, robotics, and reinforcement learning.

We further research on the acceleration phenomenon on Riemannian manifolds by introducing the first global first-order method that achieves the same rates as accelerated gradient descent in the Euclidean space for the optimization of smooth and geodesically convex (g-convex) or strongly g-convex functions defined on the hyperbolic space or a subset of the sphere, up to constants and log factors. To the best of our knowledge, this is the first method that is proved to achieve these rates globally on functions defined on a Riemannian manifold $\mathcal{M}$ other than the Euclidean space. Additionally, for any Riemannian manifold of bounded sectional curvature, we provide reductions from optimization methods for smooth and g-convex functions to methods for smooth and strongly g-convex functions and vice versa. As a proxy, we solve a constrained non-convex Euclidean problem, under a condition between convexity and quasar-convexity.