Fast Rates for Bandit PAC Multiclass Classification
<|reference_start|>Fast Rates for Bandit PAC Multiclass Classification: We study multiclass PAC learning with bandit feedback, where inputs are classified into one of $K$ possible labels and feedback is limited to whether or not the predicted labels are correct. Our main contribution is in designing a novel learning algorithm for the agnostic $(\varepsilon,\delta)$-PAC version of the problem, with sample complexity of $O\big( (\operatorname{poly}(K) + 1 / \varepsilon^2) \log (|H| / \delta) \big)$ for any finite hypothesis class $H$. In terms of the leading dependence on $\varepsilon$, this improves upon existing bounds for the problem, that are of the form $O(K/\varepsilon^2)$. We also provide an extension of this result to general classes and establish similar sample complexity bounds in which $\log |H|$ is replaced by the Natarajan dimension. This matches the optimal rate in the full-information version of the problem and resolves an open question studied by Daniely, Sabato, Ben-David, and Shalev-Shwartz (2011) who demonstrated that the multiplicative price of bandit feedback in realizable PAC learning is $\Theta(K)$. We complement this by revealing a stark contrast with the agnostic case, where the price of bandit feedback is only $O(1)$ as $\varepsilon \to 0$. Our algorithm utilizes a stochastic optimization technique to minimize a log-barrier potential based on Frank-Wolfe updates for computing a low-variance exploration distribution over the hypotheses, and is made computationally efficient provided access to an ERM oracle over $H$.<|reference_end|>
@article{erez2024fast,
    title={Fast Rates for Bandit PAC Multiclass Classification},
    author={Liad Erez, Alon Cohen, Tomer Koren, Yishay Mansour, Shay Moran},
    journal={arXiv preprint arXiv:2406.12406},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.12406},
    primaryClass={cs.LG cs.AI stat.ML}
}