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Near Minimax Optimal Players for the Finite-Time 3-Expert Prediction Problem
Yasin Abbasi Yadkori · Peter Bartlett · Victor Gabillon

Wed Dec 06 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #59
We study minimax strategies for the online prediction problem with expert advice. It has been conjectured that a simple adversary strategy, called COMB, is near optimal in this game for any number of experts. Our results and new insights make progress in this direction by showing that, up to a small additive term, COMB is minimax optimal in the finite-time three expert problem. In addition, we provide for this setting a new near minimax optimal COMB-based learner. Prior to this work, in this problem, learners obtaining the optimal multiplicative constant in their regret rate were known only when $K=2$ or $K\rightarrow\infty$. We characterize, when $K=3$, the regret of the game scaling as $\sqrt{8/(9\pi)T}\pm \log(T)^2$ which gives for the first time the optimal constant in the leading ($\sqrt{T}$) term of the regret.

Author Information

Yasin Abbasi Yadkori (Adobe Research)
Peter Bartlett (UC Berkeley)
Peter Bartlett

Peter Bartlett is professor of Computer Science and Statistics at the University of California at Berkeley, Associate Director of the Simons Institute for the Theory of Computing, and Director of the Foundations of Data Science Institute. He has previously held positions at the Queensland University of Technology, the Australian National University and the University of Queensland. His research interests include machine learning and statistical learning theory, and he is the co-author of the book Neural Network Learning: Theoretical Foundations. He has been Institute of Mathematical Statistics Medallion Lecturer, winner of the Malcolm McIntosh Prize for Physical Scientist of the Year, and Australian Laureate Fellow, and he is a Fellow of the IMS, Fellow of the ACM, and Fellow of the Australian Academy of Science.

Victor Gabillon (QUT - ACEMS)

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