Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

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Reinforcement Learning: An Introduction

In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worst-case on-line framework. The model we study can be interpreted as a broad, abstract extension of the well-studied on-line prediction model to a general decision-theoretic setting. We show that the multiplicative weight-update Littlestone?Warmuth rule can be adapted to this model, yielding bounds that are slightly weaker in some cases, but applicable to a considerably more general class of learning problems. We show how the resulting learning algorithm can be applied to a variety of problems, including gambling, multiple-outcome prediction, repeated games, and prediction of points in Rn. In the second part of the paper we apply the multiplicative weight-update technique to derive a new boosting algorithm. This boosting algorithm does not require any prior knowledge about the performance of the weak learning algorithm. We also study generalizations of the new boosting algorithm to the problem of learning functions whose range, rather than being binary, is an arbitrary finite set or a bounded segment of the real line.

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A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of stateof-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away.

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Mastering the game of Go with deep neural networks and tree search

Ad auctions in sponsored search support ``broad match'' that allows an advertiser to target a large number of queries while bidding only on a limited number. While giving more expressiveness to advertisers, this feature makes it challenging to optimize bids to maximize their returns: choosing to bid on a query as a broad match because it provides high profit results in one bidding for related queries which may yield low or even negative profits. 
We abstract and study the complexity of the {\em bid optimization problem} which is to determine an advertiser's bids on a subset of keywords (possibly using broad match) so that her profit is maximized. In the query language model when the advertiser is allowed to bid on all queries as broad match, we present an linear programming (LP)-based polynomial-time algorithm that gets the optimal profit. In the model in which an advertiser can only bid on keywords, ie., a subset of keywords as an exact or broad match, we show that this problem is not approximable within any reasonable approximation factor unless P=NP. To deal with this hardness result, we present a constant-factor approximation when the optimal profit significantly exceeds the cost. This algorithm is based on rounding a natural LP formulation of the problem. Finally, we study a budgeted variant of the problem, and show that in the query language model, one can find two budget constrained ad campaigns in polynomial time that implement the optimal bidding strategy. Our results are the first to address bid optimization under the broad match feature which is common in ad auctions.

Bid Optimization in Broad-Match Ad auctions

We present a new data-driven model of fairness that, unlike existing static definitions of individual or group fairness is guided by the unfairness complaints received by the system. Our model supports multiple fairness criteria and takes into account their potential incompatibilities. We consider both a stochastic and an adversarial setting of our model. In the stochastic setting, we show that our framework can be naturally cast as a Markov Decision Process with stochastic losses, for which we give efficient vanishing regret algorithmic solutions. In the adversarial setting, we design efficient algorithms with competitive ratio guarantees. We also report the results of experiments with our algorithms and the stochastic framework on artificial datasets, to demonstrate their effectiveness empirically.

Beyond Individual and Group Fairness

We establish, for the rst time, lower bounds for randomized mutual exclusion algorithms (with a read-modify-write operation). Our main result is that a constant-size shared variable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of ›(log logn) bits on the size of the shared variable, which is also tight. We investigate weaker fairness conditions and derive tight (upper and lower) bounds for them as well. Surprisingly, it turns out that slightly weakening the fairness condition results in an exponential reduction in the size of the required shared variable. Our lower bounds rely on an analysis of Markov chains that may be of interest on its own and may have applications elsewhere.

Lower bounds for randomized mutual exclusion

There is a growing interest in societal concerns in machine learning systems, especially in fairness. Multicalibration gives a comprehensive methodology to address group fairness. In this work, we address the multicalibration error and decouple it from the prediction error. The importance of decoupling the fairness metric (multicalibration) and the accuracy (prediction error) is due to the inherent trade-off between the two, and the societal decision regarding the "right tradeoff" (as imposed many times by regulators). Our work gives sample complexity bounds for uniform convergence guarantees of multicalibration error, which implies that regardless of the accuracy, we can guarantee that the empirical and (true) multicalibration errors are close. We emphasize that our results: (1) are more general than previous bounds, as they apply to both agnostic and realizable settings, and do not rely on a specific type of algorithm (such as deferentially private), (2) improve over previous multicalibration sample complexity bounds and (3) implies uniform convergence guarantees for the classical calibration error.

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Sample Complexity of Uniform Convergence for Multicalibration

We consider a model of robust learning in an adversarial environment. The learner gets uncorrupted training data with access to possible corruptions that may be effected by the adversary during testing. The learner's goal is to build a robust classifier, which will be tested on future adversarial examples. The adversary is limited to $k$ possible corruptions for each input. We model the learner-adversary interaction as a zero-sum game. This model is closely related to the adversarial examples model of Schmidt et al. (2018); Madry et al. (2017). Our main results consist of generalization bounds for the binary and multiclass classification, as well as the real-valued case (regression). For the binary classification setting, we both tighten the generalization bound of Feige, Mansour, and Schapire (2015), and are also able to handle infinite hypothesis classes. The sample complexity is improved from $O(\frac{1}{\epsilon^4}\log(\frac{|\mathcal{H}|}{\delta}))$ to $O\big(\frac{1}{\epsilon^2}(\sqrt{k \mathrm{VC}(\mathcal{H})}\log^{\frac{3}{2}+\alpha}(k\mathrm{VC}(\mathcal{H}))+\log(\frac{1}{\delta})\big)$ for any $\alpha > 0$. Additionally, we extend the algorithm and generalization bound from the binary to the multiclass and real-valued cases. Along the way, we obtain results on fat-shattering dimension and Rademacher complexity of $k$-fold maxima over function classes; these may be of independent interest. 
For binary classification, the algorithm of Feige et al. (2015) uses a regret minimization algorithm and an ERM oracle as a black box; we adapt it for the multiclass and regression settings. The algorithm provides us with near-optimal policies for the players on a given training sample.

Yishay Mansour

Papers

Bid Optimization in Broad-Match Ad auctions

Beyond Individual and Group Fairness

Lower bounds for randomized mutual exclusion

Sample Complexity of Uniform Convergence for Multicalibration

Improved generalization bounds for robust learning