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Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice

6 November 2015
Francesco Orabona
D. Pál
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Abstract

We prove non-asymptotic lower bounds on the expectation of the maximum of ddd independent Gaussian variables and the expectation of the maximum of ddd independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of online learning with expert advice.

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