Recently ensemble methods like ADABOOST have been applied successfully in many problems, while seemingly defying the problems of overfitting. ADABOOST rarely overfits in the low noise regime, however, we show that it clearly does so for higher noise levels. Central to the understanding of this fact is the margin distribution. ADABOOST can be viewed as a constraint gradient descent in an error function with respect to the margin. We find that ADABOOST asymptotically achieves a hard margin distribution, i.e. the algorithm concentrates its resources on a few hard-to-learn patterns that are interestingly very similar to Support Vectors. A hard margin is clearly a sub-optimal strategy in the noisy case, and regularization, in our case a "mistrust" in the data, must be introduced in the algorithm to alleviate the distortions that single difficult patterns (e.g. outliers) can cause to the margin distribution. We propose several regularization methods and generalizations of the original ADABOOST algorithm to achieve a soft margin. In particular we suggest (1) regularized ADABOOST REG where the gradient decent is done directly with respect to the soft margin and (2) regularized linear and quadratic programming (LP/QP-) ADABOOST, where the soft margin is attained by introducing slack variables. Extensive simulations demonstrate that the proposed regularized ADABOOST-type algorithms are useful and yield competitive results for noisy data.

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In this paper, we consider the impact of cyber attacks on voltage regulation in distribution systems when a number of photovoltaic (PV) systems are connected. We employ a centralized control scheme that utilizes voltage measurements from sectionizing switches equipped with sensors. It is demonstrated that if measurements are falsified by an attacker, voltage violation can occur in the system. However, by equipping the control with a detection algorithm, we verify that the damage can be limited especially when the number of attacked sensors is small through theoretical analysis and simulation case studies. In addition, studies are made on attacks which attempt to reduce the output power at PV systems equipped with overvoltage protection functions. Further discussion is provided on how to enhance the security level of the proposed algorithm. Japan. His current research interests include networked control systems, multiagent systems, hybrid systems, cyber security of power systems, and probabilistic algorithms.Dr. Ishii has served as an Associate Editor for Automatica and previously for the IEEE TRANSACTIONS ON AUTOMATIC CONTROL. He is the Chair of the International Federation of Automatic Control Technical Committee on Networked Systems.Isao Ono received the B.Eng. degree in control engineering, and the M.Eng. and Dr.Eng. degrees in computational intelligence and systems science from the Tokyo Institute

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