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Multi-robot cooperative control has gained extensive research interest due to its wide applications in civil, security, and military domains. This paper proposes a cooperative control algorithm for multi-robot systems with general linear dynamics. The algorithm is based on distributed cooperative optimisation and output regulation, and it achieves global optimum by utilising only information shared among neighbouring robots. Technically, a high-level distributed optimisation algorithm for multi-robot systems is presented, which will serve as an optimal reference generator for each individual agent. Then, based on the distributed optimisation algorithm, an output regulation method is utilised to solve the optimal coordination problem for general linear dynamic systems. The convergence of the proposed algorithm is theoretically proved. Both numerical simulations and real-time physical robot experiments are conducted to validate the effectiveness of the proposed cooperative control algorithms.

Reliability is one of the major design criteria in Cyber-Physical Systems (CPSs). This is because of the existence of some critical applications in CPSs and their failure is catastrophic. Therefore, employing strong error detection and correction mechanisms in CPSs is inevitable. CPSs are composed of a variety of units, including sensors, networks, and microcontrollers. Each of these units is probable to be in a faulty state at any time and the occurred fault can result in erroneous output. The fault may cause the units of CPS to malfunction and eventually crash. Traditional fault-tolerant approaches include redundancy time, hardware, information, and/or software. However, these approaches impose significant overheads besides their low error coverage, which limits their applicability. In addition, the interval between error occurrence and detection is too long in these approaches. In this paper, based on Deep Reinforcement Learning (DRL), a new error detection approach is proposed that not only detects errors with high accuracy but also can perform error detection at the moment due to very low inference time. The proposed approach can categorize different types of errors from normal data and predict whether the system will fail. The evaluation results illustrate that the proposed approach has improved more than 2x in terms of accuracy and more than 5x in terms of inference time compared to other approaches.

We provide a theoretical justification for sample recovery using diffusion based image inpainting in a linear model setting. While most inpainting algorithms require retraining with each new mask, we prove that diffusion based inpainting generalizes well to unseen masks without retraining. We analyze a recently proposed popular diffusion based inpainting algorithm called RePaint (Lugmayr et al., 2022), and show that it has a bias due to misalignment that hampers sample recovery even in a two-state diffusion process. Motivated by our analysis, we propose a modified RePaint algorithm we call RePaint$^+$ that provably recovers the underlying true sample and enjoys a linear rate of convergence. It achieves this by rectifying the misalignment error present in drift and dispersion of the reverse process. To the best of our knowledge, this is the first linear convergence result for a diffusion based image inpainting algorithm.

Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them based on their importance weight. For particle filters to be computationally tractable, it must be feasible to simulate the trajectories by drawing from the sampling distribution. Simultaneously, these trajectories need to reflect the reality of the nonlinear dynamical system so that the resulting estimators are accurate. Thus, the crux of particle filters lies in designing sampling distributions that are both easy to sample from and lead to accurate estimators. In this work, we propose to learn the sampling distributions. We put forward four methods for learning sampling distributions from observed measurements. Three of the methods are parametric methods in which we learn the mean and covariance matrix of a multivariate Gaussian distribution; each methods exploits a different aspect of the data (generic, time structure, graph structure). The fourth method is a nonparametric alternative in which we directly learn a transform of a uniform random variable. All four methods are trained in an unsupervised manner by maximizing the likelihood that the states may have produced the observed measurements. Our computational experiments demonstrate that learned sampling distributions exhibit better performance than designed, minimum-degeneracy sampling distributions.

Current evaluations of Continual Learning (CL) methods typically assume that there is no constraint on training time and computation. This is an unrealistic assumption for any real-world setting, which motivates us to propose: a practical real-time evaluation of continual learning, in which the stream does not wait for the model to complete training before revealing the next data for predictions. To do this, we evaluate current CL methods with respect to their computational costs. We hypothesize that under this new evaluation paradigm, computationally demanding CL approaches may perform poorly on streams with a varying distribution. We conduct extensive experiments on CLOC, a large-scale dataset containing 39 million time-stamped images with geolocation labels. We show that a simple baseline outperforms state-of-the-art CL methods under this evaluation, questioning the applicability of existing methods in realistic settings. In addition, we explore various CL components commonly used in the literature, including memory sampling strategies and regularization approaches. We find that all considered methods fail to be competitive against our simple baseline. This surprisingly suggests that the majority of existing CL literature is tailored to a specific class of streams that is not practical. We hope that the evaluation we provide will be the first step towards a paradigm shift to consider the computational cost in the development of online continual learning methods.

Nonparametric estimation for semilinear SPDEs, namely stochastic reaction-diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid in time and space with infill asymptotics in both coordinates. Firstly, we derive a nonparametric estimator for the reaction function of the underlying equation. The estimate is chosen from a finite-dimensional function space based on a least squares criterion. Oracle inequalities provide conditions for the estimator to achieve the usual nonparametric rate of convergence. Adaptivity is provided via model selection. Secondly, we show that the asymptotic properties of realized quadratic variation based estimators for the diffusivity and volatility carry over from linear SPDEs. In particular, we obtain a rate-optimal joint estimator of the two parameters. The result relies on our precise analysis of the H\"older regularity of the solution process and its nonlinear component, which may be of its own interest. Both steps of the calibration can be carried out simultaneously without prior knowledge of the parameters.

Differing from the well-developed horizontal object detection area whereby the computing-friendly IoU based loss is readily adopted and well fits with the detection metrics. In contrast, rotation detectors often involve a more complicated loss based on SkewIoU which is unfriendly to gradient-based training. In this paper, we propose an effective approximate SkewIoU loss based on Gaussian modeing and Kalman filter, which mainly consists of two items. The first term is a scale-insensitive center point loss, which is used to quickly get the center points between bounding boxes closer to assist the second term. In the distance-independent second term, Kalman filter is adopted to inherently mimic the mechanism of SkewIoU by its definition, and show its alignment with the SkewIoU loss at trend-level within a certain distance (i.e. within 9 pixels). This is in contrast to recent Gaussian modeling based rotation detectors e.g. GWD loss and KLD loss that involve a human-specified distribution distance metric which require additional hyperparameter tuning that vary across datasets and detectors. The resulting new loss called KFIoU loss is easier to implement and works better compared with exact SkewIoU loss, thanks to its full differentiability and ability to handle the non-overlapping cases. We further extend our technique to the 3-D case which also suffers from the same issues as 2-D detection. Extensive results on various public datasets (2-D/3-D, aerial/text/face images) with different base detectors show the effectiveness of our approach.

The Boolean Satisfiability (SAT) problem stands out as an attractive NP-complete problem in theoretic computer science and plays a central role in a broad spectrum of computing-related applications. Exploiting and tuning SAT solvers under numerous scenarios require massive high-quality industry-level SAT instances, which unfortunately are quite limited in the real world. To address the data insufficiency issue, in this paper, we propose W2SAT, a framework to generate SAT formulas by learning intrinsic structures and properties from given real-world/industrial instances in an implicit fashion. To this end, we introduce a novel SAT representation called Weighted Literal Incidence Graph (WLIG), which exhibits strong representation ability and generalizability against existing counterparts, and can be efficiently generated via a specialized learning-based graph generative model. Decoding from WLIGs into SAT problems is then modeled as finding overlapping cliques with a novel hill-climbing optimization method termed Optimal Weight Coverage (OWC). Experiments demonstrate the superiority of our WLIG-induced approach in terms of graph metrics, efficiency, and scalability in comparison to previous methods. Additionally, we discuss the limitations of graph-based SAT generation for real-world applications, especially when utilizing generated instances for SAT solver parameter-tuning, and pose some potential directions.

The analysis of data stored in multiple sites has become more popular, raising new concerns about the security of data storage and communication. Federated learning, which does not require centralizing data, is a common approach to preventing heavy data transportation, securing valued data, and protecting personal information protection. Therefore, determining how to aggregate the information obtained from the analysis of data in separate local sites has become an important statistical issue. The commonly used averaging methods may not be suitable due to data nonhomogeneity and incomparable results among individual sites, and applying them may result in the loss of information obtained from the individual analyses. Using a sequential method in federated learning with distributed computing can facilitate the integration and accelerate the analysis process. We develop a data-driven method for efficiently and effectively aggregating valued information by analyzing local data without encountering potential issues such as information security and heavy transportation due to data communication. In addition, the proposed method can preserve the properties of classical sequential adaptive design, such as data-driven sample size and estimation precision when applied to generalized linear models. We use numerical studies of simulated data and an application to COVID-19 data collected from 32 hospitals in Mexico, to illustrate the proposed method.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.