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A Drifting-Games Analysis for Online Learning and Applications to Boosting
Haipeng Luo · Robert E Schapire

Wed Dec 04:00 PM -- 08:59 PM PST @ Level 2, room 210D #None

We provide a general mechanism to design online learning algorithms based on a minimax analysis within a drifting-games framework. Different online learning settings (Hedge, multi-armed bandit problems and online convex optimization) are studied by converting into various kinds of drifting games. The original minimax analysis for drifting games is then used and generalized by applying a series of relaxations, starting from choosing a convex surrogate of the 0-1 loss function. With different choices of surrogates, we not only recover existing algorithms, but also propose new algorithms that are totally parameter-free and enjoy other useful properties. Moreover, our drifting-games framework naturally allows us to study high probability bounds without resorting to any concentration results, and also a generalized notion of regret that measures how good the algorithm is compared to all but the top small fraction of candidates. Finally, we translate our new Hedge algorithm into a new adaptive boosting algorithm that is computationally faster as shown in experiments, since it ignores a large number of examples on each round.

Author Information

Haipeng Luo (Microsoft Research)
Robert E Schapire (MIcrosoft Research)

Robert Schapire received his ScB in math and computer science from Brown University in 1986, and his SM (1988) and PhD (1991) from MIT under the supervision of Ronald Rivest. After a short post-doc at Harvard, he joined the technical staff at AT&T Labs (formerly AT&T Bell Laboratories) in 1991 where he remained for eleven years. At the end of 2002, he became a Professor of Computer Science at Princeton University. His awards include the 1991 ACM Doctoral Dissertation Award, the 2003 Gödel Prize and the 2004 Kanelakkis Theory and Practice Award (both of the last two with Yoav Freund). His main research interest is in theoretical and applied machine learning.

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