Efficient Online Bandit Multiclass Learning with $\tilde{O}(\sqrt{T})$ Regret

TL;DR

This paper introduces an efficient second-order algorithm for online multiclass bandit learning that achieves near-optimal regret bounds and performs well in experiments, addressing a longstanding open problem.

Contribution

The paper proposes a novel second-order algorithm with $ ilde{O}(rac{1}{ ext{eta}}\sqrt{T})$ regret for bandit multiclass problems, covering a range of loss functions.

Findings

Achieves $ ilde{O}(rac{1}{ ext{eta}}\sqrt{T})$ regret bound.

Performs favorably against previous algorithms in experiments.

Addresses an open problem in bandit multiclass learning.

Abstract

We present an efficient second-order algorithm with $\tilde{O}(\frac{1}{\eta}\sqrt{T})$ regret for the bandit online multiclass problem. The regret bound holds simultaneously with respect to a family of loss functions parameterized by $\eta$, for a range of $\eta$ restricted by the norm of the competitor. The family of loss functions ranges from hinge loss ($\eta=0$) to squared hinge loss ($\eta=1$). This provides a solution to the open problem of (J. Abernethy and A. Rakhlin. An efficient bandit algorithm for $\sqrt{T}$-regret in online multiclass prediction? In COLT, 2009). We test our algorithm experimentally, showing that it also performs favorably against earlier algorithms.