In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria -or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multipleantenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.
Index TermsLearning, stochastic optimization, game theory, matrix exponential learning, variational stability, uncertainty.
P. Mertikopoulos is with the
Abstract-This paper investigates the use of recent visual features based on second-order statistics, as well as new processing techniques to improve the quality of features. More specifically, we present and evaluate Fisher Vectors (FV), Vectors of Locally Aggregated Descriptors (VLAD), and Vectors of Locally Aggregated Tensors (VLAT). These techniques are combined with several normalization techniques, such as power law normalization and orthogonalisation/whitening of descriptor spaces. Results on the UC Merced land use dataset shows the relevance of these new methods for land-use classification, as well as a significant improvement over Bag-of-Words.
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