Improved second-order bounds for prediction with expert advice

Abstract : This work studies external regret in sequential prediction games with arbitrary payoffs (nonnegative or non-positive). External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. We focus on two important parameters: $M$, the largest absolute value of any payoff, and $Q^*$, the sum of squared payoffs of the best action. Given these parameters we derive first a simple and new forecasting strategy with regret at most order of $\\sqrt{Q^*(\\ln N)} + M\\,\\ln N$, where $N$ is the number of actions. We extend the results to the case where the parameters are unknown and derive similar bounds. We then devise a refined analysis of the weighted majority forecaster, which yields bounds of the same flavour. The proof techniques we develop are finally applied to the adversarial multi-armed bandit setting, and we prove bounds on the performance of an online algorithm in the case where there is no lower bound on the probability of each action.
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https://hal.archives-ouvertes.fr/hal-00007539
Contributor : Gilles Stoltz <>
Submitted on : Friday, July 15, 2005 - 5:09:16 PM
Last modification on : Tuesday, April 2, 2019 - 2:16:16 PM

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  • HAL Id : hal-00007539, version 1

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Nicolo Cesa-Bianchi, Yishay Mansour, Gilles Stoltz. Improved second-order bounds for prediction with expert advice. 2005, pp.217-232. ⟨hal-00007539⟩

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