  This paper introduces a new online learning framework for multiclass
classification called learning with diluted bandit feedback. At every time
step, the algorithm predicts a candidate label set instead of a single label
for the observed example. It then receives feedback from the environment
whether the actual label lies in this candidate label set or not. This feedback
is called "diluted bandit feedback". Learning in this setting is even more
challenging than the bandit feedback setting, as there is more uncertainty in
the supervision. We propose an algorithm for multiclass classification using
dilute bandit feedback (MC-DBF), which uses the exploration-exploitation
strategy to predict the candidate set in each trial. We show that the proposed
algorithm achieves O(T^{1-\frac{1}{m+2}}) mistake bound if candidate label set
size (in each step) is m. We demonstrate the effectiveness of the proposed
approach with extensive simulations.
