Beyond Bandit Feedback in Online Multiclass Classification

Dirk van der Hoeven, Federico Fusco, Nicolò Cesa-Bianchi

Keywords: Online learning, multiclass classification, bandit algorithms, surrogate losses, feedback graphs

TL;DR: We present new and improved results for the online multiclass classification setting.

Abstract:

We study the problem of online multiclass classification in a setting where the learner's feedback is determined by an arbitrary directed graph. While including bandit feedback as a special case, feedback graphs allow a much richer set of applications, including filtering and label efficient classification.
We introduce \textproc{Gappletron}, the first online multiclass algorithm that works with arbitrary feedback graphs. For this new algorithm,
we prove surrogate regret bounds that hold, both in expectation and with high probability, for a large class of surrogate losses. Our bounds are of order $B\sqrt{\rho KT}$, where $B$ is the diameter of the prediction space, $K$ is the number of classes, $T$ is the time horizon, and $\rho$ is the domination number (a graph-theoretic parameter affecting the amount of exploration). In the full information case, we show that \textproc{Gappletron} achieves a constant surrogate regret of order $B^2K$. We also prove a general lower bound of order $\max\big\{B^2K,\sqrt{T}\big\}$ showing that our upper bounds are not significantly improvable. Experiments on synthetic data show that for various feedback graphs our algorithm is competitive against known baselines.

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