In this note we derive an exact expression for the expected probability V of constraint violation in a sampled convex program (see [1], [2] for definitions and an introduction to this topic): V = expected number of support constraints/1 + number of constraints. This result (Theorem 1) is obtained using a simple technique based on cardinality count. In the note, we also use a Chernoff bounding technique on the upper tail violation probability expression derived in to obtain one of the tightest available explicit bounds on the sample complexity of sampled convex programs (Proposition 3).
A note on the expected probability of constraint violation in sampled convex programs / Calafiore, Giuseppe Carlo. - STAMPA. - (2009), pp. 1788-1791. (Intervento presentato al convegno IEEE Multi-conference on Systems and Control tenutosi a St. Petersburg, Russia nel July 8-10, 2009) [10.1109/CCA.2009.5281097].
A note on the expected probability of constraint violation in sampled convex programs
CALAFIORE, Giuseppe Carlo
2009
Abstract
In this note we derive an exact expression for the expected probability V of constraint violation in a sampled convex program (see [1], [2] for definitions and an introduction to this topic): V = expected number of support constraints/1 + number of constraints. This result (Theorem 1) is obtained using a simple technique based on cardinality count. In the note, we also use a Chernoff bounding technique on the upper tail violation probability expression derived in to obtain one of the tightest available explicit bounds on the sample complexity of sampled convex programs (Proposition 3).Pubblicazioni consigliate
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https://hdl.handle.net/11583/2284915
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