We study the stochastic contextual bandit problem, where the reward is generated from an unknown bounded function with additive noise. We propose the NeuralUCB algorithm, which leverages the representation power of deep neural networks and uses a neural network-based random feature mapping to construct an upper confidence bound (UCB) of reward for efficient exploration. We prove that, under mild assumptions, NeuralUCB achieves $\tilde O(\sqrt{T})$ regret, where $T$ is the number of rounds. To the best of our knowledge, our algorithm is the first neural network-based contextual bandit algorithm with near-optimal regret guarantee. Preliminary experiment results on synthetic data corroborate our theory, and shed light on potential applications of our algorithm to real-world problems.

--Deep Neural Networks (DNNs) are usually over-parameterized, causing excessive memory and interconnection cost on the hardware platform. Existing pruning approaches remove secondary parameters at the end of training to reduce the model size; but without exploiting the intrinsic network property, they still require the full interconnection to prepare the network. Inspired by the observation that brain networks follow the Small-World model, we propose a novel structural pruning scheme, which includes (1) hierarchically trimming the network into a Small-World model before training, (2) training the network for a given dataset, and (3) optimizing the network for accuracy. The new scheme effectively reduces both the model size and the interconnection needed before training, achieving a locally clustered and globally sparse model. We demonstrate our approach on LeNet-5 for MNIST and VGG-16 for CIF AR-10, decreasing the number of parameters to 2.3% and 9.02% of the baseline model, respectively. Recent developments in Deep Neural Networks (DNNs) have made them an integral part of modern day data processing which enable applications such as image recognition [1], object detection [2], speech recognition [3] and other applications.

In this paper, we show that the bundle method can be applied to solve semidefinite programming problems with a low rank solution without ever constructing a full matrix. To accomplish this, we use recent results from randomly sketching matrix optimization problems and from the analysis of bundle methods. Under strong duality and strict complementarity of SDP, we achieve $\tilde{O}(\frac{1}{\epsilon})$ convergence rates for both the primal and the dual sequences, and the algorithm proposed outputs a $O(\sqrt{\epsilon})$ approximate solution $\hat{X}$ (measured by distances) with a low rank representation with at most $\tilde{O}(\frac{1}{\epsilon})$ many iterations.

We study a noisy symmetric tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank symmetric tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been dedicated to this problem, prior algorithms either are computationally too expensive for large-scale applications, or come with sub-optimal statistical guarantees. Focusing on "incoherent" and well-conditioned tensors of a constant CP rank, we propose a two-stage nonconvex algorithm --- (vanilla) gradient descent following a rough initialization --- that achieves the best of both worlds. Specifically, the proposed nonconvex algorithm faithfully completes the tensor and retrieves all individual tensor factors within nearly linear time, while at the same time enjoying near-optimal statistical guarantees (i.e. minimal sample complexity and optimal estimation accuracy). The estimation errors are evenly spread out across all entries, thus achieving optimal $\ell_{\infty}$ statistical accuracy. The insight conveyed through our analysis of nonconvex optimization might have implications for other tensor estimation problems.

We analyze the trade-off between model complexity and accuracy for random forests by breaking the trees up into individual classification rules and selecting a subset of them. We show experimentally that already a few rules are sufficient to achieve an acceptable accuracy close to that of the original model. Moreover, our results indicate that in many cases, this can lead to simpler models that clearly outperform the original ones.

Precision oncology, the genetic sequencing of tumors to identify druggable targets, has emerged as the standard of care in the treatment of many cancers. Nonetheless, due to the pace of therapy development and variability in patient information, designing effective protocols for individual treatment assignment in a sample-efficient way remains a major challenge. One promising approach to this problem is to frame precision oncology treatment as a contextual bandit problem and to apply sequential decision-making algorithms designed to minimize regret in this setting. However, a clear prerequisite for considering this methodology in high-stakes clinical decisions is careful benchmarking to understand realistic costs and benefits. Here, we propose a benchmark dataset to evaluate contextual bandit algorithms based on real in vitro drug response of approximately 900 cancer cell lines. Specifically, we curated a dataset of complete treatment responses for a subset of 7 treatments from prior in vitro studies. This allows us to compute the regret of proposed decision policies using biologically plausible counterfactuals. We ran a suite of Bayesian bandit algorithms on our benchmark, and found that the methods accumulate less regret over a sequence of treatment assignment tasks than a rule-based baseline derived from current clinical practice. This effect was more pronounced when genomic information was included as context. We expect this work to be a starting point for evaluation of both the unique structural requirements and ethical implications for real-world testing of bandit based clinical decision support.

In processing and manufacturing industries, there has been a large push to produce higher quality products and ensure maximum efficiency of processes. This requires approaches to effectively detect and resolve disturbances to ensure optimal operations. While the control system can compensate for many types of disturbances, there are changes to the process which it still cannot handle adequately. It is therefore important to further develop monitoring systems to effectively detect and identify those faults such that they can be quickly resolved by operators. In this paper, a novel probabilistic fault detection and identification method is proposed which adopts a newly developed deep learning approach using Bayesian recurrent neural networks (BRNNs) with variational dropout. The BRNN model is general and can model complex nonlinear dynamics. Moreover, compared to traditional statistic-based data-driven fault detection and identification methods, the proposed BRNN-based method yields uncertainty estimates which allow for simultaneous fault detection of chemical processes, direct fault identification, and fault propagation analysis. The outstanding performance of this method is demonstrated and contrasted to (dynamic) principal component analysis, which are widely applied in the industry, in the benchmark Tennessee Eastman process (TEP) and a real chemical manufacturing dataset.

We present the first provably convergent off-policy actor-critic algorithm (COF-PAC) with function approximation in a two-timescale form. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Difference Learning and Emphatic Temporal Difference Learning. With the help of the emphasis critic and the canonical value function critic, we show convergence for COF-PAC, where the critics are linear and the actor can be nonlinear.

Electroencephalography (EEG) data are difficult to obtain due to complex experimental setups and reduced comfort with prolonged wearing. This poses challenges to train powerful deep learning model with the limited EEG data. B eing able to generate EEG data computationally could address this limitation . We propose a novel Wasserstein Generative Adversarial Network with gradient penalty ( W GAN - GP) to synthesize EEG data. We further extend ed this network to a class - conditioned variant that also includes a classification branch to perform event - related classification. We trained the proposed networks to generate one and 64 - channel data resembling EEG signals routinely seen in a rapid serial visual presentation (RSVP) experiment and demonstrate d the validity of the generated samples . We also tested intra - subject cross - session classification performance for classifying the RSVP target events and show ed that class - conditioned W GAN - GP can achieve improved event - classification performance over EEGNet . LECTROENCEPHAL OGRAPHY (EEG) i s an attractive neuroimaging tool for measuring brain activities due to its portability, noninvasiveness and its ability to capture spatiotemporal dynamics of human brains . However, obtaining high - quality EEG data could be labor - intensive an d costly. The scarcity of high - quality EEG data poses significant challenges in the era of deep learning (DL) to train high - performing deep models to predict cognitive events and understand associated brain dynamics and mechanisms. It is thus of great interest in developing cost - effective approaches to augment the limited EEG samples so that the superb ability of DL in learning data representation can be fully exploited for EEG - based cognitive event classification.

We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system dynamics should be contractive on the average with respect to the Lyapunov function and large enough small sets should exist with large enough minorization constants. We also establish that a law of large numbers holds for bounded functionals of the process. Applications to queuing systems and to machine learning algorithms are presented.