Article2001

Competitive On‐line Statistics

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226 citations0/0 files storedInternational Statistical Review

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Advanced Bandit Algorithms Research Statistical Methods and Inference Machine Learning and Algorithms

Abstract

Summary A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive on‐line algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid's prequential statistics). In this approach, which we call “competitive on‐line statistics”, it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive on‐line statistical procedures areguaranteedto hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss.

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References

1997A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting 1997Exponentiated Gradient versus Gradient Descent for Linear Predictors 2002Gambling in a rigged casino: The adversarial multi-armed bandit problem 1997How to use expert advice 1991Universal Portfolios 1998Tracking the Best Expert 1999Adaptive Game Playing Using Multiplicative Weights 1996Game theory, on-line prediction and boosting

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