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In a wide variety of applications including online advertising, contractual hiring, and wireless scheduling, the controller is constrained by a stringent budget constraint on the available resources, which are consumed in a random amount by each action, and a stochastic feasibility constraint that may impose important operational limitations on decision-making. In this work, we consider a general model to address such problems, where each action returns a random reward, cost, and penalty from an unknown joint distribution, and the decision-maker aims to maximize the total reward under a budget constraint $B$ on the total cost and a stochastic constraint on the time-average penalty. We propose a novel low-complexity algorithm based on Lyapunov optimization methodology, named ${\tt LyOn}$, and prove that for $K$ arms it achieves $O(\sqrt{K B\log B})$ regret and zero constraint-violation when $B$ is sufficiently large. The low computational cost and sharp performance bounds of ${\tt LyOn}$ suggest that Lyapunov-based algorithm design methodology can be effective in solving constrained bandit optimization problems.

We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test. In outlier hypothesis testing, one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task is to discern the set of outlying sequences that are generated according to anomalous distributions. The nominal and anomalous distributions are \emph{unknown}. We consider the case of multiple outliers where the number of outliers is unknown and each outlier can follow a different anomalous distribution. Under this setting, we study the tradeoff among the probabilities of misclassification error, false alarm and false reject. Specifically, we propose a threshold-based test that ensures exponential decay of misclassification error and false alarm probabilities. We study two constraints on the false reject probability, with one constraint being that it is a non-vanishing constant and the other being that it has an exponential decay rate. For both cases, we characterize bounds on the false reject probability, as a function of the threshold, for each tuple of nominal and anomalous distributions. Finally, we demonstrate the asymptotic optimality of our test under the generalized Neyman-Pearson criterion.

Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms, is \emph{probability sampling}. It creates a sampled data set by including each data point from the original data set with a known probability. Although the benefit of running machine learning algorithms on the reduced data set is obvious, one major concern is that the performance of the solution obtained from samples might be much worse than that of the optimal solution when using the full data set. In this paper, we examine the performance loss caused by probability sampling in the context of adaptive submodular maximization. We consider a simple probability sampling method which selects each data point with probability at least $r\in[0,1]$. If we set $r=1$, our problem reduces to finding a solution based on the original full data set. We define sampling gap as the largest ratio between the optimal solution obtained from the full data set and the optimal solution obtained from the samples, over independence systems. Our main contribution is to show that if the sampling probability of each data point is at least $r$ and the utility function is policywise submodular, then the sampling gap is both upper bounded and lower bounded by $1/r$. We show that the property of policywise submodular can be found in a wide range of real-world applications, including pool-based active learning and adaptive viral marketing.

\emph{$K$-best enumeration}, which asks to output $k$ best solutions without duplication, plays an important role in data analysis for many fields. In such fields, data can be typically represented by graphs, and thus subgraph enumeration has been paid much attention to. However, $k$-best enumeration tends to be intractable since, in many cases, finding one optimum solution is \NP-hard. To overcome this difficulty, we combine $k$-best enumeration with a new concept of enumeration algorithms called \emph{approximation enumeration algorithms}, which has been recently proposed. As a main result, we propose an $\alpha$-approximation algorithm for minimal connected edge dominating sets which outputs $k$ minimal solutions with cardinality at most $\alpha\cdot\overline{\rm OPT}$, where $\overline{\rm OPT}$ is the cardinality of a mini\emph{mum} solution which is \emph{not} outputted by the algorithm, and $\alpha$ is constant. Moreover, our proposed algorithm runs in $O(nm^2\Delta)$ delay, where $n$, $m$, $\Delta$ are the number of vertices, the number of edges, and the maximum degree of an input graph.

This paper concerns the verification of continuous-time polynomial spline trajectories against linear temporal logic specifications (LTL without 'next'). Each atomic proposition is assumed to represent a state space region described by a multivariate polynomial inequality. The proposed approach samples a trajectory strategically, to capture every one of its region transitions. This yields a discrete word called a trace, which is amenable to established formal methods for path checking. The original continuous-time trajectory is shown to satisfy the specification if and only if its trace does. General topological conditions on the sample points are derived that ensure a trace is recorded for arbitrary continuous paths, given arbitrary region descriptions. Using techniques from computer algebra, a trace generation algorithm is developed to satisfy these conditions when the path and region boundaries are defined by polynomials. The proposed PolyTrace algorithm has polynomial complexity in the number of atomic propositions, and is guaranteed to produce a trace of any polynomial path. Its performance is demonstrated via numerical examples and a case study from robotics.

We address the problem of anomaly detection in videos. The goal is to identify unusual behaviours automatically by learning exclusively from normal videos. Most existing approaches are usually data-hungry and have limited generalization abilities. They usually need to be trained on a large number of videos from a target scene to achieve good results in that scene. In this paper, we propose a novel few-shot scene-adaptive anomaly detection problem to address the limitations of previous approaches. Our goal is to learn to detect anomalies in a previously unseen scene with only a few frames. A reliable solution for this new problem will have huge potential in real-world applications since it is expensive to collect a massive amount of data for each target scene. We propose a meta-learning based approach for solving this new problem; extensive experimental results demonstrate the effectiveness of our proposed method.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

In one-class-learning tasks, only the normal case (foreground) can be modeled with data, whereas the variation of all possible anomalies is too erratic to be described by samples. Thus, due to the lack of representative data, the wide-spread discriminative approaches cannot cover such learning tasks, and rather generative models, which attempt to learn the input density of the foreground, are used. However, generative models suffer from a large input dimensionality (as in images) and are typically inefficient learners. We propose to learn the data distribution of the foreground more efficiently with a multi-hypotheses autoencoder. Moreover, the model is criticized by a discriminator, which prevents artificial data modes not supported by data, and enforces diversity across hypotheses. Our multiple-hypothesesbased anomaly detection framework allows the reliable identification of out-of-distribution samples. For anomaly detection on CIFAR-10, it yields up to 3.9% points improvement over previously reported results. On a real anomaly detection task, the approach reduces the error of the baseline models from 6.8% to 1.5%.

Accurate detection and tracking of objects is vital for effective video understanding. In previous work, the two tasks have been combined in a way that tracking is based heavily on detection, but the detection benefits marginally from the tracking. To increase synergy, we propose to more tightly integrate the tasks by conditioning the object detection in the current frame on tracklets computed in prior frames. With this approach, the object detection results not only have high detection responses, but also improved coherence with the existing tracklets. This greater coherence leads to estimated object trajectories that are smoother and more stable than the jittered paths obtained without tracklet-conditioned detection. Over extensive experiments, this approach is shown to achieve state-of-the-art performance in terms of both detection and tracking accuracy, as well as noticeable improvements in tracking stability.

Several approaches to image stitching use different constraints to estimate the motion model between image pairs. These constraints can be roughly divided into two categories: geometric constraints and photometric constraints. In this paper, geometric and photometric constraints are combined to improve the alignment quality, which is based on the observation that these two kinds of constraints are complementary. On the one hand, geometric constraints (e.g., point and line correspondences) are usually spatially biased and are insufficient in some extreme scenes, while photometric constraints are always evenly and densely distributed. On the other hand, photometric constraints are sensitive to displacements and are not suitable for images with large parallaxes, while geometric constraints are usually imposed by feature matching and are more robust to handle parallaxes. The proposed method therefore combines them together in an efficient mesh-based image warping framework. It achieves better alignment quality than methods only with geometric constraints, and can handle larger parallax than photometric-constraint-based method. Experimental results on various images illustrate that the proposed method outperforms representative state-of-the-art image stitching methods reported in the literature.