We present RepRank, an unsupervised graph-based ranking model for extractive multi-document summarization in which the similarity between words, sentences, and word-to-sentence can be estimated by the distances between their vector representations in a unified vector space. In order to obtain desirable representations, we propose a self-attention based learning method that represent a sentence by the weighted sum of its word embeddings, and the weights are concentrated to those words hopefully better reflecting the content of a document. We show that salient sentences and keywords can be extracted in a joint and mutual reinforcement process using our learned representations, and prove that this process always converges to a unique solution leading to improvement in performance. A variant of absorbing random walk and the corresponding sampling-based algorithm are also described to avoid redundancy and increase diversity in the summaries. Experiment results with multiple benchmark datasets show that RepRank achieved the best or comparable performance in ROUGE.

Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the regularized mean field optimization problem to a so-called mean field Schrodinger dynamics. We develop an energy-dissipation method to show that the marginal distributions of the mean field Schrodinger dynamics converge exponentially quickly towards the unique minimizer of the regularized optimization problem. Remarkably, the mean field Schrodinger dynamics is proved to be a gradient flow on the probability measure space with respect to the relative entropy. Finally we propose a Monte Carlo method to sample the marginal distributions of the mean field Schrodinger dynamics.

In the digital transformation era, integrating digital technology into every aspect of banking operations improves process automation, cost efficiency, and service level improvement. Although logistics for Automated Teller Machine (ATM) cash is a crucial task that impacts operating costs and consumer satisfaction, there has been little effort to enhance it. Specifically, in Vietnam, with a market of more than 20,000 ATMs nationally, research and technological solutions that can resolve this issue remain scarce. In this paper, we generalized the vehicle routing problem for ATM cash replenishment, suggested a mathematical model, and then offered a tool to evaluate various situations. When being evaluated on the simulated dataset, our proposed model and method produced encouraging results with the benefits of cutting ATM cash operating costs.

In this paper, we simultaneously tackle the problem of energy optimal and safe navigation of electric vehicles in a data-driven robust optimization framework. We consider a dynamic model of the electric vehicle which includes kinematic variables in both inertial and body coordinate systems in order to capture both longitudinal and lateral motion as well as state-of-energy of the battery. We leverage past data of obstacle motion to construct a future occupancy set with probabilistic guarantees, and formulate robust collision avoidance constraints with respect to such an occupancy set using convex programming duality. Consequently, we present the finite horizon optimal control problem subject to robust collision avoidance constraints while penalizing resulting energy consumption. Finally, we show the effectiveness of the proposed approach in reducing energy consumption and ensuring safe navigation via extensive simulations involving curved roads and multiple obstacles.

Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar. Due to its importance and NP-hardness, a lot of methods have been proposed, among which evolutionary algorithms are a class of popular ones. Evolutionary clustering has found many successful applications, but all the results are empirical, lacking theoretical support. This paper fills this gap by proving that the approximation performance of the GSEMO (a simple multi-objective evolutionary algorithm) for solving four formulations of clustering, i.e., $k$-tMM, $k$-center, discrete $k$-median and $k$-means, can be theoretically guaranteed. Furthermore, we consider clustering under fairness, which tries to avoid algorithmic bias, and has recently been an important research topic in machine learning. We prove that for discrete $k$-median clustering under individual fairness, the approximation performance of the GSEMO can be theoretically guaranteed with respect to both the objective function and the fairness constraint.

Many problems in robotics, such as estimating the state from noisy sensor data or aligning two point clouds, can be posed and solved as least-squares problems. Unfortunately, vanilla nonminimal solvers for least-squares problems are notoriously sensitive to outliers. As such, various robust loss functions have been proposed to reduce the sensitivity to outliers. Examples of loss functions include pseudo-Huber, Cauchy, and Geman-McClure. Recently, these loss functions have been generalized into a single loss function that enables the best loss function to be found adaptively based on the distribution of the residuals. However, even with the generalized robust loss function, most nonminimal solvers can only be solved locally given a prior state estimate due to the nonconvexity of the problem. The first contribution of this paper is to combine graduated nonconvexity (GNC) with the generalized robust loss function to solve least-squares problems without a prior state estimate and without the need to specify a loss function. Moreover, existing loss functions, including the generalized loss function, are based on Gaussian-like distribution. However, residuals are often defined as the squared norm of a multivariate error and distributed in a Chi-like fashion. The second contribution of this paper is to apply a norm-aware adaptive robust loss function within a GNC framework. The proposed approach enables a GNC formulation of a generalized loss function such that GNC can be readily applied to a wider family of loss functions. Furthermore, simulations and experiments demonstrate that the proposed method is more robust compared to non-GNC counterparts, and yields faster convergence times compared to other GNC formulations.

A new algorithm for regret minimization in online convex optimization is described. The regret of the algorithm after $T$ time periods is $O(\sqrt{T \log T})$ - which is the minimum possible up to a logarithmic term. In addition, the new algorithm is adaptive, in the sense that the regret bounds hold not only for the time periods $1,\ldots,T$ but also for every sub-interval $s,s+1,\ldots,t$. The running time of the algorithm matches that of newly introduced interior point algorithms for regret minimization: in $n$-dimensional space, during each iteration the new algorithm essentially solves a system of linear equations of order $n$, rather than solving some constrained convex optimization problem in $n$ dimensions and possibly many constraints.

The Bipartite Polarization Problem is an optimization problem where the goal is to find the highest polarized bipartition on a weighted and labelled graph that represents a debate developed through some social network, where nodes represent user's opinions and edges agreement or disagreement between users. This problem can be seen as a generalization of the maxcut problem, and in previous work approximate solutions and exact solutions have been obtained for real instances obtained from Reddit discussions, showing that such real instances seem to be very easy to solve. In this paper, we investigate further the complexity of this problem, by introducing an instance generation model where a single parameter controls the polarization of the instances in such a way that this correlates with the average complexity to solve those instances. The average complexity results we obtain are consistent with our hypothesis: the higher the polarization of the instance, the easier is to find the corresponding polarized bipartition.

Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example, users might be interested in finding alternative feature sets with similar prediction quality, offering different explanations of the data. In this article, we introduce alternative feature selection and formalize it as an optimization problem. In particular, we define alternatives via constraints and enable users to control the number and dissimilarity of alternatives. Next, we analyze the complexity of this optimization problem and show NP-hardness. Further, we discuss how to integrate conventional feature-selection methods as objectives. Finally, we evaluate alternative feature selection with 30 classification datasets. We observe that alternative feature sets may indeed have high prediction quality, and we analyze several factors influencing this outcome.

Athletic robots demand a whole-body actuation system design that utilizes motors up to the boundaries of their performance. However, creating such robots poses challenges of integrating design principles and reasoning of practical design choices. This paper presents a design framework that guides designers to find optimal design choices to create an actuation system that can rapidly generate torques and velocities required to achieve a given set of tasks, by minimizing inertia and leveraging cooperation between actuators. The framework serves as an interactive tool for designers who are in charge of providing design rules and candidate components such as motors, reduction mechanism, and coupling mechanisms between actuators and joints. A binary integer linear optimization explores design combinations to find optimal components that can achieve a set of tasks. The framework is demonstrated with 200 optimal design studies of a biped with 5-degree-of-freedom (DoF) legs, focusing on the effect of achieving multiple tasks (walking, lifting), constraining the mass budget of all motors in the system and the use of coupling mechanisms. The result provides a comprehensive view of how design choices and rules affect reflected inertia, copper loss of motors, and force capability of optimal actuation systems.