# Bounds on Individual Risk for Log-loss Predictors

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Peter D. Grünwald,
Wojciech Kotłowski
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Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:813-816, 2011.

#### Abstract

In sequential prediction with log-loss as well as density estimationwith risk measured by KL divergence, one is often interested in the\em expected instantaneous loss, or, equivalently, the \em individual risk at a given fixed sample size n. For Bayesianprediction and estimation methods, it is often easy to obtain boundson the \em cumulative risk. Such results are based on bounding theindividual sequence regret, a technique that is very well known in theCOLT community. Motivated by the easiness of proofs for the cumulativerisk, our open problem is to use the results on cumulative risk to prove corresponding individual-risk bounds.

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