Dmitry Panchenko

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Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to “difficult” control problems. Unfortunately, the number of samples required in order to guarantee stringent performance levels may be prohibitively large. This paper introduces bootstrap learning methods and the concept of stopping times to(More)
We conjecture that the Parisi functional in the Sherrington-Kirkpatrick model is convex in the functional order parameter. We prove a partial result that shows the convexity along “one-sided” directions. An interesting consequence of this result is the log-convexity of Lm norm for a class of random variables. 1 A problem and some results. Let M be a set of(More)
In order to study certain questions concerning the distribution of the overlap in Sherrington–Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the free energy of multiple systems with constrained overlaps. One can write analogues of Guerra's replica symmetry breaking bound for such systems but it is not at(More)
We introduce and study several measures of complexity of functions from the convex hull of a given base class. These complexity measures take into account the sparsity of the weights of a convex combination as well as certain clustering properties of the base functions involved in it. We prove new upper confidence bounds on generalization error of ensemble(More)