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Life sciences · Preprint
arXiv · September 18, 2026
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We prove that the optimal expected mistake bound of online learning a function class $\mathcal{H}$ by a randomized proper learning algorithm is $O(\mathtt{L}(\mathcal{H}) \log T)$, where $\mathtt{L}(\mathcal{H})$ is the Littlestone dimension of $\mathcal{H}$ and $T$ is the time horizon. Our result improves upon the previously best known bound of $O(\mathtt{L}(\mathcal{H}) \log^6 T)$ given by Daskalakis and Golowich (STOC 2022), and is optimal up to a universal constant for worst-case classes.