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# A lower bound for a prediction algorithm under the Kullback-Leibler game

*Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications*, PMLR 152:39-51, 2021.

#### Abstract

We obtain a lower bound for an algorithm predicting finite-dimensional distributions (i.e., points from a simplex) under Kullback-Leibler loss. The bound holds w.r.t. the class of softmax linear predictors. We then show that the bound is asymptotically matched by the Bayesian universal algorithm.