Uniform regret bounds over R^d for the sequential linear regression problem with the square loss

05/29/2018

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by   Pierre Gaillard, et al.

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We consider the setting of online linear regression for arbitrary deterministic sequences, with the square loss. We are interested in regret bounds that hold uniformly over all vectors in u ∈ R^d. Vovk (2001) showed a d ln T lower bound on this uniform regret. We exhibit forecasters with closed-form regret bounds that match this d ln T quantity. To the best of our knowledge, earlier works only provided closed-form regret bounds of 2d ln T + O(1).