, Volume 90, Issue 3, pp 347-383
Date: 24 Oct 2012

Multiclass classification with bandit feedback using adaptive regularization

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We present a new multiclass algorithm in the bandit framework, where after making a prediction, the learning algorithm receives only partial feedback, i.e., a single bit indicating whether the predicted label is correct or not, rather than the true label. Our algorithm is based on the second-order Perceptron, and uses upper-confidence bounds to trade-off exploration and exploitation, instead of random sampling as performed by most current algorithms. We analyze this algorithm in a partial adversarial setting, where instances are chosen adversarially, while the labels are chosen according to a linear probabilistic model which is also chosen adversarially. We show a regret of \(\mathcal{O}(\sqrt{T}\log T)\) , which improves over the current best bounds of \(\mathcal{O}(T^{2/3})\) in the fully adversarial setting. We evaluate our algorithm on nine real-world text classification problems and on four vowel recognition tasks, often obtaining state-of-the-art results, even compared with non-bandit online algorithms, especially when label noise is introduced.

Editor: Adam Tauman Kalai.