Archivio Istituzionale della RicercaIn this paper, we present a recursive algorithm for the solution of uncertain least-square problems in a stochastic setting. The algorithm aims at minimizing the expected value with respect to the uncertainty of the least-square residual, and returns with high probability an ε-suboptimal solution in a pre-specified number of iterations. The proposed technique is based on minimization of the empirical mean and on uniform convergence results derived from learning theory inequalities. Comparisons with gradient algorithms for stochastic optimization are also discussed in the paper.
Near Optimal Stochastic Solution to Uncertain Least Squares Problems / Calafiore, Giuseppe Carlo; F., Dabbene. - STAMPA. - 5:(2003), pp. 3803-3808. (Intervento presentato al convegno American Control Conference tenutosi a Denver nel 4-6 June 2003) [10.1109/ACC.2003.1240427].
Near Optimal Stochastic Solution to Uncertain Least Squares Problems
CALAFIORE, Giuseppe Carlo;
2003
Abstract
In this paper, we present a recursive algorithm for the solution of uncertain least-square problems in a stochastic setting. The algorithm aims at minimizing the expected value with respect to the uncertainty of the least-square residual, and returns with high probability an ε-suboptimal solution in a pre-specified number of iterations. The proposed technique is based on minimization of the empirical mean and on uniform convergence results derived from learning theory inequalities. Comparisons with gradient algorithms for stochastic optimization are also discussed in the paper.
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https://hdl.handle.net/11583/1408974
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