This paper deals with the sampled scenarios approach to robust convex programming. It has been shown in previous works that by randomly sampling a sufficient number of constraints among the (possibly) infinite constraints of a robust convex program, one obtains a standard convex optimization problem whose solution is 'approximately feasible', in a probabilistic sense, for the original robust convex program. This is a generalization property in the learning theoretic sense, since the satisfaction of a certain number of 'training' constraints entails the satisfaction of other 'unseen' constraints. In this paper we provide a new efficient bound on the generalization rate of sampled convex programs, and show an example of application to a robust control design problem.

A New Bound on the Generalization Rate of Sampled Convex Programs / Calafiore, Giuseppe Carlo; M. C., Campi. - STAMPA. - 5:(2004), pp. 5328-5333. (Intervento presentato al convegno 43rd IEEE Conference on Decision and Control tenutosi a Bahamas nel 14-17 Dec. 2004) [10.1109/CDC.2004.1429655].

A New Bound on the Generalization Rate of Sampled Convex Programs

CALAFIORE, Giuseppe Carlo;
2004

Abstract

This paper deals with the sampled scenarios approach to robust convex programming. It has been shown in previous works that by randomly sampling a sufficient number of constraints among the (possibly) infinite constraints of a robust convex program, one obtains a standard convex optimization problem whose solution is 'approximately feasible', in a probabilistic sense, for the original robust convex program. This is a generalization property in the learning theoretic sense, since the satisfaction of a certain number of 'training' constraints entails the satisfaction of other 'unseen' constraints. In this paper we provide a new efficient bound on the generalization rate of sampled convex programs, and show an example of application to a robust control design problem.
2004
0780386825
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1409001
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