Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
EMNLP '02 Proceedings of the ACL-02 conference on Empirical methods in natural language processing - Volume 10
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Multi-Pass Geometric Algorithms
Discrete & Computational Geometry
Algorithms for distributed functional monitoring
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Rank minimization via online learning
Proceedings of the 25th international conference on Machine learning
Bundle Methods for Regularized Risk Minimization
The Journal of Machine Learning Research
Neural Network Learning: Theoretical Foundations
Neural Network Learning: Theoretical Foundations
Optimal sampling from distributed streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Distributed training strategies for the structured perceptron
HLT '10 Human Language Technologies: The 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Scaling up Machine Learning: Parallel and Distributed Approaches
Scaling up Machine Learning: Parallel and Distributed Approaches
Optimal distributed online prediction using mini-batches
The Journal of Machine Learning Research
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A recent paper [1] proposes a general model for distributed learning that bounds the communication required for learning classifiers with ε error on linearly separable data adversarially distributed across nodes. In this work, we develop key improvements and extensions to this basic model. Our first result is a two-party multiplicative-weight-update based protocol that uses O(d2 log1/ε) words of communication to classify distributed data in arbitrary dimension d, ε-optimally. This extends to classification over k nodes with O(kd2 log1/ε) words of communication. Our proposed protocol is simple to implement and is considerably more efficient than baselines compared, as demonstrated by our empirical results. In addition, we show how to solve fixed-dimensional and high-dimensional linear programming with small communication in a distributed setting where constraints may be distributed across nodes. Our techniques make use of a novel connection from multipass streaming, as well as adapting the multiplicative- weight-update framework more generally to a distributed setting.