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We study the problem of discrete distribution estimation in KL divergence andprovide concentration bounds for the Laplace estimator. We show that thedeviation from mean scales as $\sqrt{k}/n$ when $n \ge k$, improving upon thebest prior result of $k/n$. We also establish a matching lower bound that showsthat our bounds are tight up to polylogarithmic factors.

Concentration Bounds for Discrete Distribution Estimation in KL Divergence