Learning with Randomized Majority Votes

We propose algorithms for producing weighted majority votes that learn by probing the empirical risk of a randomized (uniformly weighted) majority vote—instead of probing the zero-one loss, at some margin level, of the deterministic weighted majority vote as it is often proposed. The learning algorithms minimize a risk bound which is convex in the weights. Our numerical results indicate that learners producing a weighted majority vote based on the empirical risk of the randomized majority vote at some finite margin have no significant advantage over learners that achieve this same task based on the empirical risk at zero margin. We also find that it is sufficient for learners to minimize only the empirical risk of the randomized majority vote at a fixed number of voters without considering explicitly the entropy of the distribution of voters. Finally, our extensive numerical results indicate that the proposed learning algorithms are producing weighted majority votes that generally compare favorably to those produced by AdaBoost.