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From PACBayes bounds to KL regularization
 Advances in Neural Information Processing Systems 22
, 2009
"... We show that convex KLregularized objective functions are obtained from a PACBayes risk bound when using convex loss functions for the stochastic Gibbs classifier that upperbound the standard zeroone loss used for the weighted majority vote. By restricting ourselves to a class of posteriors, tha ..."
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We show that convex KLregularized objective functions are obtained from a PACBayes risk bound when using convex loss functions for the stochastic Gibbs classifier that upperbound the standard zeroone loss used for the weighted majority vote. By restricting ourselves to a class of posteriors, that we call quasi uniform, we propose a simple coordinate descent learning algorithm to minimize the proposed KLregularized cost function. We show that standard ℓpregularized objective functions currently used, such as ridge regression and ℓpregularized boosting, are obtained from a relaxation of the KL divergence between the quasi uniform posterior and the uniform prior. We present numerical experiments where the proposed learning algorithm generally outperforms ridge regression and AdaBoost. 1
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 1 Fractional Norm Regularization: Learning With Very
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Robust Forward Algorithms via PACBayes and Laplace Distributions
"... Laplace random variables are commonly used to model extreme noise in many fields, while systems trained to deal with such noises are often characterized by robustness properties. We introduce new learning algorithms that minimize objectives derived directly from PACBayes bounds, incorporating Lapla ..."
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Laplace random variables are commonly used to model extreme noise in many fields, while systems trained to deal with such noises are often characterized by robustness properties. We introduce new learning algorithms that minimize objectives derived directly from PACBayes bounds, incorporating Laplace distributions. The resulting algorithms are regulated by the Huber loss function and are robust to noise, as the Laplace distribution integrated large deviation of parameters. We analyze the convexity properties of the objective, and propose a few bounds which are fully convex, two of which jointly convex in the mean and standarddeviation under certain conditions. We derive new forward algorithms analogous to recent boosting algorithms, providing novel relations between boosting and PACBayes analysis. Experiments show that our algorithms outperform AdaBoost, L1LogBoost [10], and RobustBoost [11] in a wide range of input noise. 1
Regularized Reinforcement Learning with Performance Guarantees
, 2014
"... To my wife, parents and supporting friends. ii ACKNOWLEDGEMENTS I would like to thank all members of McGill’s Reasoning and Learning lab who provided me with useful thoughts and ideas throughout my graduate studies. I am particularly thankful to my supervisor, Joelle Pineau, for her relentless help ..."
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To my wife, parents and supporting friends. ii ACKNOWLEDGEMENTS I would like to thank all members of McGill’s Reasoning and Learning lab who provided me with useful thoughts and ideas throughout my graduate studies. I am particularly thankful to my supervisor, Joelle Pineau, for her relentless help and support over this time. I would also like to thank Doina Precup for her invaluable contributions to my research and studies at McGill University. Special thanks goes to Yuri Grinberg, Amirmassoud Farahmand and Csaba Szepesvári for their contributions to my research and publications. I am also thankful to PierreLuc Bacon for his help in writing the French abstract, and Angus Leigh for being an awesome labmate. iii Reinforcement learning covers a broad category of control problems in which
DÉPARTEMENT D’INFORMATIQUE ET DE GÉNIE LOGICIEL FACULTÉ DES SCIENCES ET DE GÉNIE
"... à la Faculté des études supérieures et postdoctorales de l’Université Laval dans le cadre du programme de doctorat en informatique pour l’obtention du grade de PhilosophiæDoctor (Ph.D.) ..."
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à la Faculté des études supérieures et postdoctorales de l’Université Laval dans le cadre du programme de doctorat en informatique pour l’obtention du grade de PhilosophiæDoctor (Ph.D.)