Statistics Papers

Document Type

Technical Report

Date of this Version

1-28-2007

Publication Source

EECS Department, University of California, Berkeley

Abstract

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the "ideal" algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.

Comments

At the time of publication, author Alexander Rakhlin was affiliated with the University of California, Berkeley. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

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Date Posted: 27 November 2017