This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In this setting, we derive new and sharper regret bounds for the well-known exponentially weighted average forecaster and for a new forecaster with a different multiplicative update rule. Our analysis has two main advantages: first, no preliminary knowledge about the payoff sequence is needed, not even its range; second, our bounds are expressed in terms of sums of squared payoffs, replacing larger first-order quantities appearing in previous bounds. In addition, our most refined bounds have the natural and desirable property of being stable under rescalings and general translations of the payoff sequence.

Improved second-order bounds for prediction with expert advice / N. Cesa-Bianchi, Y. Mansour, G. Stoltz - In: Learning Theory: 18th Annual Conference on Learning Theory, COLT 2005 : Bertinoro, Italy, June 27-30, 2005 : Proceedings / [a cura di] P. Auer, R. Meir. - Berlin : Springer, 2005. - ISBN 3540265562. - pp. 217-232 (( Intervento presentato al 18. convegno Annual Conference on Learning Theory - COLT 2005 tenutosi a Bertinoro nel 2005.

Improved second-order bounds for prediction with expert advice

N. Cesa-Bianchi
Primo
;
2005

Abstract

This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In this setting, we derive new and sharper regret bounds for the well-known exponentially weighted average forecaster and for a new forecaster with a different multiplicative update rule. Our analysis has two main advantages: first, no preliminary knowledge about the payoff sequence is needed, not even its range; second, our bounds are expressed in terms of sums of squared payoffs, replacing larger first-order quantities appearing in previous bounds. In addition, our most refined bounds have the natural and desirable property of being stable under rescalings and general translations of the payoff sequence.
Settore INF/01 - Informatica
2005
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/9906
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