Quantum computers can offer dramatic improvements over classical devices for data analysis tasks such as prediction and classification. However, less is known about the advantages that quantum computers may bring in the setting of reinforcement learning, where learning is achieved via interaction with a task environment. Here, we consider a special case of reinforcement learning, where the task environment allows quantum access. In addition, we impose certain "naturalness" conditions on the task environment, which rule out the kinds of oracle problems that are studied in quantum query complexity (and for which quantum speedups are well-known). Within this framework of quantum-accessible reinforcement learning environments, we demonstrate that quantum agents can achieve exponential improvements in learning efficiency, surpassing previous results that showed only quadratic improvements. A key step in the proof is to construct task environments that encode well-known oracle problems, such as Simon's problem and Recursive Fourier Sampling, while satisfying the above "naturalness" conditions for reinforcement learning. Our results suggest that quantum agents may perform well in certain game-playing scenarios, where the game has recursive structure, and the agent can learn by playing against itself.

ABSTRACT This paper investigates the impact of word-based RNN language models (RNN-LMs) on the performance of end-to-end automatic speech recognition (ASR). In our prior work, we have proposed a multilevel LM, in which character-based and word-based RNN-LMs are combined in hybrid CTC/attention-based ASR. Although this multilevel approach achieves significant error reduction in the Wall Street Journal (WSJ) task, two different LMs need to be trained and used for decoding, which increase the computational cost and memory usage. In this paper, we further propose a novel wordbased RNN-LM, which allows us to decode with only the wordbased LM, where it provides look-ahead word probabilities to predict next characters instead of the character-based LM, leading competitive accuracy with less computation compared to the multilevel LM. We demonstrate the efficacy of the word-based RNN-LMs using a larger corpus, LibriSpeech, in addition to WSJ we used in the prior work. Furthermore, we show that the proposed model achieves 5.1 %WER for WSJ Eval'92 test set when the vocabulary size is increased, which is the best WER reported for end-to-end ASR systems on this benchmark. Index Terms-- End-to-end speech recognition, language modeling, decoding, connectionist temporal classification, attention decoder 1. INTRODUCTION Automatic speech recognition (ASR) is currently a mature set of widely-deployed technologies that enable successful user interface applications such as voice search [1]. However, current systems lean heavily on the scaffolding of complicated legacy architectures that grew up around traditional techniques, including hidden Markov models (HMMs), Gaussian mixture models (GMMs), hybrid HMM/deep neural network (DNN) systems, and sequence discriminative training methods [2].

We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a hierarchical manner using a simple reparameterizable distribution whose variational parameters are defined by arbitrarily flexible deep neural networks. Unlike previous works, UIVI directly optimizes the evidence lower bound (ELBO) rather than an approximation to the ELBO. We demonstrate UIVI on several models, including Bayesian multinomial logistic regression and variational autoencoders, and show that UIVI achieves both tighter ELBO and better predictive performance than existing approaches at a similar computational cost.

We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is related to the spectral properties of the Markov chain. We show that there exists a wide statistical window, in terms of sample complexity for hypothesis testing between different pairs of initial distributions. We illustrate these results in several concrete examples.

We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic MDPs with $S$ states, $A$ actions, and mixing time parameter $t_{\rm mix}$. These bounds are the first regret bounds in the general, non-episodic setting with an optimal dependence on all given parameters. They could only be improved by using an alternative mixing time parameter.

We consider the problem of learning Relational Logistic Regression (RLR). Unlike standard logistic regression, the features of RLRs are first-order formulae with associated weight vectors instead of scalar weights. We turn the problem of learning RLR to learning these vector-weighted formulae and develop a learning algorithm based on the recently successful functional-gradient boosting methods for probabilistic logic models. We derive the functional gradients and show how weights can be learned simultaneously in an efficient manner. Our empirical evaluation on standard and novel data sets demonstrates the superiority of our approach over other methods for learning RLR.

Many researches demonstrated that the DNA methylation, which occurs in the context of a CpG, has strong correlation with diseases, including cancer. There is a strong interest in analyzing the DNA methylation data to find how to distinguish different subtypes of the tumor. However, the conventional statistical methods are not suitable for analyzing the highly dimensional DNA methylation data with bounded support. In order to explicitly capture the properties of the data, we design a deep neural network, which composes of several stacked binary restricted Boltzmann machines, to learn the low dimensional deep features of the DNA methylation data. Experiments show these features perform best in breast cancer DNA methylation data cluster analysis, comparing with some state-of-the-art methods.

Wi-Fi) and the second/third/fourth generation (2/3/4G) mobile network, the number of mobile phones, which is 7.74 billion, 103.5 per 100 inhabitants all over the world in 2017, is rising dramatically [1]. Nowadays, mobile phone can not only send voice and text messages, but also easily and conveniently access the Internet which has been recognized as the most revolutionary development of Mobile Internet (M-Internet). Meanwhile, worldwide active mobile-broadband subscriptions in 2017 have increased to 4.22 billion, which is 9.21% higher than that in 2016 [1]. Figure 1 shows the numbers of mobile-cellular telephone and active mobile-broadband subscriptions of the world and main districts from 2010 to 2017. The numbers which are up to the bars are the mobile-cellular telephone or active mobile-broadband subscriptions (million) in the world of the year which increase each year. Under the M-Internet, various kinds of content (image, voice, video, etc.) can be sent and received everywhere and the related applications emerge to satisfy people's requirements, including working, study, daily life, entertainment, education, healthcare, etc. In China, mobile applications giants, i.e., Baidu, Alibaba and Tencent, held 78% of M-Internet online time per day in App which was about 2,412 minutes in 2017 [2]. This figure indicates that M-Internet has entered a rapidly growth stage.

We present an approximate Bayesian inference approach for estimating the intensity of a inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the model using a latent marked Poisson process and P\'olya--Gamma random variables we obtain a representation of the likelihood which is conjugate to the GP prior. We approximate the posterior using a free--form mean field approximation together with the framework of sparse GPs. Furthermore, as alternative approximation we suggest a sparse Laplace approximation of the posterior, for which an efficient expectation--maximisation algorithm is derived to find the posterior's mode. Results of both algorithms compare well with exact inference obtained by a Markov Chain Monte Carlo sampler and standard variational Gauss approach, while being one order of magnitude faster.

We formulate simple assumptions, implying the Robbins-Monro conditions for the $Q$-learning algorithm with the local learning rate, depending on the number of visits of a particular state-action pair (local clock) and the number of iteration (global clock). It is assumed that the Markov decision process is communicating and the learning policy ensures the persistent exploration. The restrictions are imposed on the functional dependence of the learning rate on the local and global clocks. The result partially confirms the conjecture of Bradkte (1994).