Beyond Bandit Feedback in Online Multiclass Classification
This work addresses a generalization of bandit feedback for online learning, enabling richer applications like filtering, but it is incremental as it extends existing methods to handle arbitrary graphs.
The paper tackles online multiclass classification with arbitrary feedback graphs, introducing Gappletron as the first algorithm for this setting and proving surrogate regret bounds of order B√(ρKT) and a constant regret of order B²K in full information cases, with experiments showing competitiveness against baselines.
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 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 $B\sqrt{ρKT}$, where $B$ is the diameter of the prediction space, $K$ is the number of classes, $T$ is the time horizon, and $ρ$ is the domination number (a graph-theoretic parameter affecting the amount of exploration). In the full information case, we show that 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.