Optimal Randomized Proper Online Learning

Abstract: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.

Machine Learning (cs.LG)

arXiv:2609.21445 [cs.LG]

(or arXiv:2609.21445v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.21445 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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