Online Learning: Sufficient Statistics and the Burkholder Method
Dylan J. Foster,
Alexander Rakhlin,
Karthik Sridharan
Abstract:We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain "sufficient statistics" for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these sufficient statistics, not the entire data sequence, so that the online strategy is only required to keep the sufficient statistics in memory. This characterization is achieved by bringing the full pow… Show more
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