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Meta-regularization: An approach to adaptive choice of the learning rate in gradient descent

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arXiv 2021年

作者： Xie, Guangzeng Jin, Hao Lin, Dachao Zhang, Zhihua Peking University Beijing China

We propose Meta-Regularization, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning rate, and casts the joint updating process of parameters and learning rates into a maxmin problem. Given any regularization term, our approach facilitates the generation of practical algorithms. When Meta-Regularization takes the -divergence as a regularizer, the resulting algorithms exhibit comparable theoretical convergence performance with other first-order gradient-based algorithms. Furthermore, we theoretically prove that some well-designed regularizers can improve the convergence performance under the strong-convexity condition of the objective function. Numerical experiments on benchmark problems demonstrate the effectiveness of algorithms derived from some common -divergence in full batch as well as online learning settings. Copyright © 2021, The Authors. All rights reserved.

关键词： learning algorithms

Efficient learning with arbitrary covariate shift

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arXiv 2021年

作者： Kalai, Adam Kanade, Varun Microsoft Research New England United States University of Oxford United Kingdom

We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This is the generic form of what is called covariate shift, which is impossible in general as arbitrary P and Q may not even overlap. However, recently guarantees were given in a model called PQ-learning (Goldwasser et al., 2020) where the learner has: (a) access to unlabeled test examples from Q (in addition to labeled samples from P, i.e., semi-supervised learning);and (b) the option to reject any example and abstain from classifying it (i.e., selective classification). The algorithm of Goldwasser et al. (2020) requires an (agnostic) noise-tolerant learner for C. The present work gives a polynomial-time PQ-learning algorithm, called Slice-and-Dice, that uses an oracle to a "reliable" learner for C, where reliable learning (Kalai et al., 2012) is a model of learning with one-sided noise. Furthermore, this reduction is optimal in the sense that we show the equivalence of reliable and PQ learning. Copyright © 2021, The Authors. All rights reserved.

关键词： learning algorithms

Online learning for stochastic shortest path model via posterior sampling

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arXiv 2021年

作者： Jafarnia-Jahromi, Mehdi Chen, Liyu Jain, Rahul Luo, Haipeng University of Southern California United States

We consider the problem of online reinforcement learning for the Stochastic Shortest Path (SSP) problem modeled as an unknown MDP with an absorbing state. We propose PSRL-SSP, a simple posterior sampling-based reinforcement learning algorithm for the SSP problem. The algorithm operates in epochs. At the beginning of each epoch, a sample is drawn from the posterior distribution on the unknown model dynamics, and the optimal policy with respect to the drawn sample is followed during that epoch. An epoch completes if either the number of visits to the goal state in the current epoch exceeds that of the previous epoch, or the number of visits to any of the state-action pairs is doubled. We establish a Bayesian regret bound of O(B∗S √AK), where B∗ is an upper bound on the expected cost of the optimal policy, S is the size of the state space, A is the size of the action space, and K is the number of episodes. The algorithm only requires the knowledge of the prior distribution, and has no hyper-parameters to tune. It is the first such posterior sampling algorithm and outperforms numerically previously proposed optimism-based algorithms. © 2021, CC BY.

关键词： learning algorithms

ENFORCING FAIRNESS in PRIVATE FEDERATED learning VIA the MODIFIED METHOD of DIFFERENTIAL MULTIPLIERS

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arXiv 2021年

作者： Rodríguez-Gálvez, Borja Granqvist, Filip Van Dalen, Rogier Seigel, Matt Apple United States

Federated learning with differential privacy, or private federated learning, provides a strategy to train machine learning models while respecting users' privacy. However, differential privacy can disproportionately degrade the performance of the models on under-represented groups, as these parts of the distribution are difficult to learn in the presence of noise. Existing approaches for enforcing fairness in machine learning models have considered the centralized setting, in which the algorithm has access to the users' data. This paper introduces an algorithm to enforce group fairness in private federated learning, where users' data does not leave their devices. First, the paper extends the modified method of differential multipliers to empirical risk minimization with fairness constraints, thus providing an algorithm to enforce fairness in the central setting. Then, this algorithm is extended to the private federated learning setting. The proposed algorithm, FPFL, is tested on a federated version of the Adult dataset and an "unfair" version of the FEMNIST dataset. The experiments on these datasets show how private federated learning accentuates unfairness in the trained models, and how FPFL is able to mitigate such unfairness. Copyright © 2021, The Authors. All rights reserved.

关键词： learning algorithms

learning rates for multi-task regularization networks

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arXiv 2021年

作者： Gui, Jie Zhang, Haizhang School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China Guangdong Province Key Laboratory of Computational Science Sun Yat-sen University Zhuhai519082 China

Multi-task learning is an important trend of machine learning in facing the era of artificial intelligence and big data. Despite a large amount of researches on learning rate estimates of various single-task machine learning algorithms, there is little parallel work for multi-task learning. We present mathematical analysis on the learning rate estimate of multi-task learning based on the theory of vector-valued reproducing kernel Hilbert spaces and matrix-valued reproducing kernels. For the typical multi-task regularization networks, an explicit learning rate dependent both on the number of sample data and the number of tasks is obtained. It reveals that the generalization ability of multi-task learning algorithms is indeed affected as the number of tasks increases. Keywords: vector-valued reproducing kernel Hilbert spaces, multi-task learning, matrix-valued reproducing kernels, learning rates, regularization networks. Copyright © 2021, The Authors. All rights reserved.

关键词： learning algorithms

Identification of nonlinear dynamic systems using type-2 fuzzy neural networks - A novel learning algorithm and a comparative study

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arXiv 2021年

作者： Kayacan, Erkan Kayacan, Erdal Khanesar, Mojtaba Ahmadieh Kasteelpark Arenberg 30 LeuvenB-3001 Belgium The School of Mechanical & Aerospace Engineering Nanyang Technological University 50 Nanyang Avenue Singapore639798 Singapore The Department of Electrical and Control Engineering Semnan University Semnan Iran

In order to achieve faster and more robust convergence (especially under noisy working environments), a sliding mode theory-based learning algorithm has been proposed to tune both the premise and consequent parts of type-2 fuzzy neural networks in this paper. Differently from recent studies, where sliding mode control theory-based rules are proposed for only the consequent part of the network, the developed algorithm applies fully sliding mode parameter update rules for both the premise and consequent parts of the type-2 fuzzy neural networks. In addition, the responsible parameter for sharing the contributions of the lower and upper parts of the type-2 fuzzy membership functions is also tuned. Moreover, the learning rate of the network is updated during the online training. The stability of the proposed learning algorithm has been proved by using an appropriate Lyapunov function. Several comparisons have been realized and shown that the proposed algorithm has faster convergence speed than the existing methods such as gradient-based and swarm intelligence-based methods. Moreover, the proposed learning algorithm has a closed form, and it is easier to implement than the other existing methods. © 2021, CC BY.

关键词： learning algorithms

learning to ground multi-agent communication with autoencoders

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arXiv 2021年

作者： Lin, Toru Huh, Minyoung Stauffer, Chris Lim, Ser-Nam Isola, Phillip MIT CSAIL Facebook AI

Communication requires having a common language, a lingua franca, between agents. This language could emerge via a consensus process, but it may require many generations of trial and error. Alternatively, the lingua franca can be given by the environment, where agents ground their language in representations of the observed world. We demonstrate a simple way to ground language in learned representations, which facilitates decentralized multi-agent communication and coordination. We find that a standard representation learning algorithm – autoencoding – is sufficient for arriving at a grounded common language. When agents broadcast these representations, they learn to understand and respond to each other’s utterances and achieve surprisingly strong task performance across a variety of multi-agent communication environments. © 2021, CC BY.

关键词： learning algorithms

Mean-field methods and algorithmic perspectives for high-dimensional machine learning

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arXiv 2021年

作者： Aubin, Benjamin Institut de Physique Théorique CEA Université Paris-Saclay Saclay France

At a time when the use of data has reached an unprecedented level, machine learning, and more specifically deep learning based on artificial neural networks, has been responsible for very important practical advances. Their use is now ubiquitous in many fields of application, from image classification, text mining to speech recognition, including time series prediction and text analysis. However, the understanding of many algorithms used in practice is mainly empirical and their behavior remains difficult to analyze. These theoretical gaps raise many questions about their effectiveness and potential risks. Establishing theoretical foundations on which to base numerical observations has become one of the fundamental challenges of the scientific community. The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this manuscript, we revisit an approach based on the tools of statistical physics of disordered systems. Developed through a rich literature, they have been precisely designed to infer the macroscopic behavior of a large number of particles from their microscopic interactions. At the heart of this work, we strongly capitalize on the deep connection between the replica method and message passing algorithms in order to shed light on the phase diagrams of various theoretical models, with an emphasis on the potential differences between statistical and algorithmic thresholds. We essentially focus on synthetic tasks and data generated in the teacher-student paradigm. In particular, we apply these mean-field methods to the Bayes-optimal analysis of committee machines, to the worst-case analysis of Rademacher generalization bounds for perceptrons, and to empirical risk minimization in the context of generalized linear models. Finally, we develop a framework to analyze estimation models with structured prior informations, produced for instance by d

关键词： learning algorithms

Privacy-preserving serverless edge learning with decentralized small data

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arXiv 2021年

作者： Lin, Shih-Chun Lin, Chia-Hung North Carolina State University United States

—In the last decade, data-driven algorithms outperformed traditional optimization-based algorithms in many research areas, such as computer vision, natural language processing, etc. However, extensive data usages bring a new challenge or even threat to deep learning algorithms, i.e., privacy-preserving. Distributed training strategies have recently become a promising approach to ensure data privacy when training deep models. This paper extends conventional serverless platforms with serverless edge learning architectures and provides an efficient distributed training framework from the networking perspective. This framework dynamically orchestrates available resources among heterogeneous physical units to efficiently fulfill deep learning objectives. The design jointly considers learning task requests and underlying infrastructure heterogeneity, including last-mile transmissions, computation abilities of mobile devices, edge and cloud computing centers, and devices’ battery status. Furthermore, to significantly reduce distributed training overheads, small-scale data training is proposed by integrating with a general, simple data classifier. This low-load enhancement can seamlessly work with various distributed deep models to improve communications and computation efficiencies during the training phase. Finally, open challenges and future research directions encourage the research community to develop efficient distributed deep learning techniques. Copyright © 2021, The Authors. All rights reserved.

关键词： learning algorithms