Cooperative Online Learning: Keeping your Neighbors Updated

We study an asynchronous online learning setting with a network of agents. At each time step, some of the agents are activated, requested to make a prediction, and pay the corresponding loss. The loss function is then revealed to these agents and also to their neighbors in the network. Our results characterize how much knowing the network structure affects the regret as a function of the model of agent activations. When activations are stochastic, the optimal regret (up to constant factors) is shown to be of order $\sqrt{\alpha T}$, where $T$ is the horizon and $\alpha$ is the independence number of the network. We prove that the upper bound is achieved even when agents have no information about the network structure. When activations are adversarial the situation changes dramatically: if agents ignore the network structure, a $\Omega(T)$ lower bound on the regret can be proven, showing that learning is impossible. However, when agents can choose to ignore some of their neighbors based on the knowledge of the network structure, we prove a $O(\sqrt{\overline{\chi} T})$ sublinear regret bound, where $\overline{\chi} \ge \alpha$ is the clique-covering number of the network

Learning with online constraints : shifting concepts and active learning

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 99-102).Many practical problems such as forecasting, real-time decision making, streaming data applications, and resource-constrained learning, can be modeled as learning with online constraints. This thesis is concerned with analyzing and designing algorithms for learning under the following online constraints: i) The algorithm has only sequential, or one-at-time, access to data. ii) The time and space complexity of the algorithm must not scale with the number of observations. We analyze learning with online constraints in a variety of settings, including active learning. The active learning model is applicable to any domain in which unlabeled data is easy to come by and there exists a (potentially difficult or expensive) mechanism by which to attain labels. First, we analyze a supervised learning framework in which no statistical assumptions are made about the sequence of observations, and algorithms are evaluated based on their regret, i.e. their relative prediction loss with respect to the hindsight-optimal algorithm in a comparator class. We derive a, lower bound on regret for a class of online learning algorithms designed to track shifting concepts in this framework. We apply an algorithm we provided in previous work, that avoids this lower bound, to an energy-management problem in wireless networks, and demonstrate this application in a network simulation.(cont.) Second, we analyze a supervised learning framework in which the observations are assumed to be iid, and algorithms are compared by the number of prediction mistakes made in reaching a target generalization error. We provide a lower bound on mistakes for Perceptron, a standard online learning algorithm, for this framework. We introduce a modification to Perceptron and show that it avoids this lower bound, and in fact attains the optimal mistake-complexity for this setting. Third, we motivate and analyze an online active learning framework. The observations are assumed to be iid, and algorithms are judged by the number of label queries to reach a target generalization error. Our lower bound applies to the active learning setting as well, as a lower bound on labels for Perceptron paired with any active learning rule. We provide a new online active learning algorithm that avoids the lower bound, and we upper bound its label-complexity. The upper bound is optimal and also bounds the algorithm's total errors (labeled and unlabeled). We analyze the algorithm further, yielding a label-complexity bound under relaxed assumptions. Using optical character recognition data, we empirically compare the new algorithm to an online active learning algorithm with data-dependent performance guarantees, as well as to the combined variants of these two algorithms.by Claire E. Monteleoni.Ph.D

Online Active Learning in Practice

We compare the practical performance of several recently proposed algorithms for active learning in the online setting. We consider two algorithms (and their combined variants) that are strongly online, in that they do not store any previously labeled examples, and for which formal guarantees have recently been proven under various assumptions. We perform an empirical evaluation on optical character recognition (OCR) data, an application that we argue to be appropriately served by online active learning. We compare the performance between the algorithm variants and show significant reductions in label-complexity over random sampling

Differentially Private Empirical Risk Minimization

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the $\epsilon$-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance.Comment: 40 pages, 7 figures, accepted to the Journal of Machine Learning Researc

Online Learning of Non-stationary Sequences

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. The performance of each expert may change over time in a manner unknown to the learner. We formulate a class of universal learning algorithms for this problem by expressing them as simple Bayesian algorithms operating on models analogous to Hidden Markov Models (HMMs). We derive a new performance bound for such algorithms which is considerably simpler than existing bounds. The bound provides the basis for learning the rate at which the identity of the optimal expert switches over time. We find an analytic expression for the a priori resolution at which we need to learn the rate parameter. We extend our scalar switching-rate result to models of the switching-rate that are governed by a matrix of parameters, i.e. arbitrary homogeneous HMMs. We apply and examine our algorithm in the context of the problem of energy management in wireless networks. We analyze the new results in the framework of Information Theory

Learning with Online Constraints: Shifting Concepts and Active Learning

PhD thesisMany practical problems such as forecasting, real-time decisionmaking, streaming data applications, and resource-constrainedlearning, can be modeled as learning with online constraints. Thisthesis is concerned with analyzing and designing algorithms forlearning under the following online constraints: 1) The algorithm hasonly sequential, or one-at-time, access to data. 2) The time andspace complexity of the algorithm must not scale with the number ofobservations. We analyze learning with online constraints in avariety of settings, including active learning. The active learningmodel is applicable to any domain in which unlabeled data is easy tocome by and there exists a (potentially difficult or expensive)mechanism by which to attain labels.First, we analyze a supervised learning framework in which nostatistical assumptions are made about the sequence of observations,and algorithms are evaluated based on their regret, i.e. theirrelative prediction loss with respect to the hindsight-optimalalgorithm in a comparator class. We derive a lower bound on regretfor a class of online learning algorithms designed to track shiftingconcepts in this framework. We apply an algorithm we provided inprevious work, that avoids this lower bound, to an energy-managementproblem in wireless networks, and demonstrate this application in anetwork simulation. Second, we analyze a supervised learning frameworkin which the observations are assumed to be iid, and algorithms arecompared by the number of prediction mistakes made in reaching atarget generalization error. We provide a lower bound on mistakes forPerceptron, a standard online learning algorithm, for this framework.We introduce a modification to Perceptron and show that it avoids thislower bound, and in fact attains the optimal mistake-complexity forthis setting.Third, we motivate and analyze an online active learning framework.The observations are assumed to be iid, and algorithms are judged bythe number of label queries to reach a target generalizationerror. Our lower bound applies to the active learning setting as well,as a lower bound on labels for Perceptron paired with any activelearning rule. We provide a new online active learning algorithm thatavoids the lower bound, and we upper bound its label-complexity. Theupper bound is optimal and also bounds the algorithm's total errors(labeled and unlabeled). We analyze the algorithm further, yielding alabel-complexity bound under relaxed assumptions. Using opticalcharacter recognition data, we empirically compare the new algorithmto an online active learning algorithm with data-dependent performanceguarantees, as well as to the combined variants of these twoalgorithms

Climate Informatics: Accelerating Discovering in Climate Science with Machine Learning

The goal of climate informatics, an emerging discipline, is to inspire collaboration between climate scientists and data scientists, in order to develop tools to analyze complex and ever-growing amounts of observed and simulated climate data, and thereby bridge the gap between data and understanding. Here, recent climate informatics work is presented, along with details of some of the field's remaining challenges. Given the impact of climate change, understanding the climate system is an international priority. The goal of climate informatics is to inspire collaboration between climate scientists and data scientists, in order to develop tools to analyze complex and ever-growing amounts of observed and simulated climate data, and thereby bridge the gap between data and understanding. Here, recent climate informatics work is presented, along with details of some of the remaining challenges

Technological Innovation, Data Analytics, and Environmental Enforcement

Technical innovation is ubiquitous in contemporary society and contributes to its extraordinarily dynamic character. Sometimes these innovations have significant effects on the environment or on human health. They may also stimulate efforts to develop second-order technologies to ameliorate those effects. The development of the automobile and its impact on life in the United States and throughout the world is an example. The story of modern environmental regulation more generally includes chapters filled with examples of similar efforts to respond to an enormous array of technological advances. This Article uses a different lens to consider the role of technological innovation. In particular, it considers how technological advances have the potential to shape governance efforts in the compliance realm. The Article demonstrates that such technological advances-especially new and improved monitoring capacity, advances in information dissemination through e-reporting and other techniques, and improved capacity to analyze information-have significant potential to transform governance efforts to promote compliance. Such transformation is likely to affect not only the how of compliance promotion, but also the who -- who is involved in promoting compliance. Technological innovation is likely to contribute to new thinking about the roles key actors can and should play in promoting compliance with legal norms. The Article discusses some of the potential benefits of these types of technological innovation in the context of the Environmental Protection Agency\u27s ongoing efforts to improve its compliance efforts by taking advantage of emerging technologies. We also identify some of the pitfalls or challenges that agencies such as the Environmental Protection Agency need to be aware of in opening this emerging bundle of new tools and making use of them to address real-world environmental needs