Beyond Bandit Feedback in Online Multiclass Classification

TL;DR

This paper introduces Gappletron, an online multiclass classification algorithm that effectively handles arbitrary feedback graphs, providing strong regret bounds and demonstrating competitive performance in synthetic experiments.

Contribution

We propose Gappletron, the first algorithm for online multiclass classification with arbitrary feedback graphs, and establish its theoretical regret bounds and practical competitiveness.

Findings

Regret bounds of order B√ρKT in expectation and high probability.

Constant surrogate regret of order B²K in full information setting.

Lower bound of order max{B²K, √T} showing near-optimality.

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 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 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.