23,011 research outputs found
Price decomposition in large-scale stochastic optimal control
We are interested in optimally driving a dynamical system that can be
influenced by exogenous noises. This is generally called a Stochastic Optimal
Control (SOC) problem and the Dynamic Programming (DP) principle is the natural
way of solving it. Unfortunately, DP faces the so-called curse of
dimensionality: the complexity of solving DP equations grows exponentially with
the dimension of the information variable that is sufficient to take optimal
decisions (the state variable). For a large class of SOC problems, which
includes important practical problems, we propose an original way of obtaining
strategies to drive the system. The algorithm we introduce is based on
Lagrangian relaxation, of which the application to decomposition is well-known
in the deterministic framework. However, its application to such closed-loop
problems is not straightforward and an additional statistical approximation
concerning the dual process is needed. We give a convergence proof, that
derives directly from classical results concerning duality in optimization, and
enlghten the error made by our approximation. Numerical results are also
provided, on a large-scale SOC problem. This idea extends the original DADP
algorithm that was presented by Barty, Carpentier and Girardeau (2010)
Non-uniform Feature Sampling for Decision Tree Ensembles
We study the effectiveness of non-uniform randomized feature selection in
decision tree classification. We experimentally evaluate two feature selection
methodologies, based on information extracted from the provided dataset:
\emph{leverage scores-based} and \emph{norm-based} feature selection.
Experimental evaluation of the proposed feature selection techniques indicate
that such approaches might be more effective compared to naive uniform feature
selection and moreover having comparable performance to the random forest
algorithm [3]Comment: 7 pages, 7 figures, 1 tabl
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