Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

We consider the numerical calculation of several matrix eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a quadratic form subject to linear constraints and determining the eigenvalues of a matrix which is modified by a matrix of rank one. We also consider several inverse eigenvalue problems. This includes the problem of determining the coefficients for the Gauss–Radau and Gauss–Lobatto quadrature rules. In addition, we study several eigenvalue problems which arise in least squares.

Some modified matrix eigenvalue problems.

We discuss deep reinforcement learning in an overview style. We draw a big picture, filled with details. We discuss six core elements, six important mechanisms, and twelve applications, focusing on contemporary work, and in historical contexts. We start with background of artificial intelligence, machine learning, deep learning, and reinforcement learning (RL), with resources. Next we discuss RL core elements, including value function, policy, reward, model, exploration vs. exploitation, and representation. Then we discuss important mechanisms for RL, including attention and memory, unsupervised learning, hierarchical RL, multi-agent RL, relational RL, and learning to learn. After that, we discuss RL applications, including games, robotics, natural language processing (NLP), computer vision, finance, business management, healthcare, education, energy, transportation, computer systems, and, science, engineering, and art. Finally we summarize briefly, discuss challenges and opportunities, and close with an epilogue.

Deep reinforcement learning

Typical techniques for video captioning follow the encoder-decoder framework, which can only focus on one source video being processed. A potential disadvantage of such design is that it cannot capture the multiple visual context information of a word appearing in more than one relevant videos in training data. To tackle this limitation, we propose the Memory-Attended Recurrent Network (MARN) for video captioning, in which a memory structure is designed to explore the full-spectrum correspondence between a word and its various similar visual contexts across videos in training data. Thus, our model is able to achieve a more comprehensive understanding for each word and yield higher captioning quality. Furthermore, the built memory structure enables our method to model the compatibility between adjacent words explicitly instead of asking the model to learn implicitly, as most existing models do. Extensive validation on two real-word datasets demonstrates that our MARN consistently outperforms state-of-the-art methods.

/pdf/memory-attended-recurrent-network-for-video-captioning-3a37agkhhm.pdf

Memory-Attended Recurrent Network for Video Captioning

We make three contributions toward better understanding policy gradient methods in the tabular setting. First, we show that with the true gradient, policy gradient with a softmax parametrization converges at a $O(1/t)$ rate, with constants depending on the problem and initialization. This result significantly expands the recent asymptotic convergence results. The analysis relies on two findings: that the softmax policy gradient satisfies a Łojasiewicz inequality, and the minimum probability of an optimal action during optimization can be bounded in terms of its initial value. Second, we analyze entropy regularized policy gradient and show that it enjoys a significantly faster linear convergence rate $O(e^{-t})$ toward softmax optimal policy. This result resolves an open question in the recent literature. Finally, combining the above two results and additional new $\Omega(1/t)$ lower bound results, we explain how entropy regularization improves policy optimization, even with the true gradient, from the perspective of convergence rate. The separation of rates is further explained using the notion of non-uniform Łojasiewicz degree. These results provide a theoretical understanding of the impact of entropy and corroborate existing empirical studies.

/pdf/on-the-global-convergence-rates-of-softmax-policy-gradient-27v2prs2ho.pdf

On the Global Convergence Rates of Softmax Policy Gradient Methods

Despite its potential to improve sample complexity versus model-free approaches, model-based reinforcement learning can fail catastrophically if the model is inaccurate. An algorithm should ideally be able to trust an imperfect model over a reasonably long planning horizon, and only rely on model-free updates when the model errors get infeasibly large. In this paper, we investigate techniques for choosing the planning horizon on a state-dependent basis, where a state's planning horizon is determined by the maximum cumulative model error around that state. We demonstrate that these state-dependent model errors can be learned with Temporal Difference methods, based on a novel approach of temporally decomposing the cumulative model errors. Experimental results show that the proposed method can successfully adapt the planning horizon to account for state-dependent model accuracy, significantly improving the efficiency of policy learning compared to model-based and model-free baselines.

/pdf/learning-to-combat-compounding-error-in-model-based-48b9akz1nh.pdf

Learning to Combat Compounding-Error in Model-Based Reinforcement Learning

The softmax is the standard transformation used in machine learning to map realvalued vectors to categorical distributions. Unfortunately, this transform poses serious drawbacks for gradient descent (ascent) optimization. We reveal this difficulty by establishing two negative results: (1) optimizing any expectation with respect to the softmax must exhibit sensitivity to parameter initialization (“softmax gravity well”), and (2) optimizing log-probabilities under the softmax must exhibit slow convergence (“softmax damping”). Both findings are based on an analysis of convergence rates using the Non-uniform Łojasiewicz (NŁ) inequalities. To circumvent these shortcomings we investigate an alternative transformation, the escort mapping, that demonstrates better optimization properties. The disadvantages of the softmax and the effectiveness of the escort transformation are further explained using the concept of NŁ coefficient. In addition to proving bounds on convergence rates to firmly establish these results, we also provide experimental evidence for the superiority of the escort transformation.

/pdf/escaping-the-gravitational-pull-of-softmax-sqoamyf108.pdf

Escaping the Gravitational Pull of Softmax

This paper proposes and evaluates Memory-Augmented Monte Carlo Tree Search (M-MCTS), which provides a new approach to exploit generalization in online real-time search. The key idea of M-MCTS is to incorporate MCTS with a memory structure, where each entry contains information of a particular state. This memory is used to generate an approximate value estimation by combining the estimations of similar states. We show that the memory based value approximation is better than the vanilla Monte Carlo estimation with high probability under mild conditions. We evaluate M-MCTS in the game of Go. Experimental results show that M-MCTS outperforms the original MCTS with the same number of simulations.

https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/download/17139/15841

Memory-Augmented Monte Carlo Tree Search

In this paper, we investigate Exploratory Conservative Policy Optimization (ECPO), a policy optimization strategy that improves exploration behavior while assuring monotonic progress in a principled objective. ECPO conducts maximum entropy exploration within a mirror descent framework, but updates policies using reversed KL projection. This formulation bypasses undesirable mode seeking behavior and avoids premature convergence to sub-optimal policies, while still supporting strong theoretical properties such as guaranteed policy improvement. Experimental evaluations demonstrate that the proposed method significantly improves practical exploration and surpasses the empirical performance of state-of-the art policy optimization methods in a set of benchmark tasks.

/pdf/on-principled-entropy-exploration-in-policy-optimization-1sbwn4xjdc.pdf

Chenjun Xiao

Papers

On the Global Convergence Rates of Softmax Policy Gradient Methods

Learning to Combat Compounding-Error in Model-Based Reinforcement Learning

Escaping the Gravitational Pull of Softmax

Memory-Augmented Monte Carlo Tree Search

On principled entropy exploration in policy optimization