The Offset Tree for Learning with Partial Labels

We present an algorithm, called the Offset Tree, for learning in situations where a loss associated with different decisions is not known, but was randomly probed. The algorithm is an {optimal} reduction from this problem to binary classification. In particular, it has regret at most $(k-1)$ times the regret of the binary classifier it uses, where $k$ is the number of decisions, and no reduction to binary classification can do better. This reduction is also computationally optimal, both at training and test time, requiring just $O(\log_2 k)$ work to train on an example or make a prediction. We test the Offset Tree empirically and discover that it generally results in better performance than several plausible alternative approaches.