Comparing Few to Rank Many: Active Human Preference Learning Using Randomized Frank-Wolfe Method

We study learning of human preferences from a limited comparison feedback. This task is ubiquitous in machine learning. Its applications such as reinforcement learning from human feedback, have been transformational. We formulate this problem as learning a Plackett-Luce model over a universe of N choices from K-way comparison feedback, where typically K ≪ N . Our solution is the D-optimal design for the Plackett-Luce objective. The design defines a data logging policy that elicits comparison feedback for a small collection of optimally chosen points from all N K feasible subsets. The main algorithmic challenge in this work is that even fast methods for solving D-optimal designs would have O( N K ) time complexity. To address this issue, we propose a randomized Frank-Wolfe (FW) algorithm that solves the linear maximization sub-problems in the FW method on randomly chosen variables. We analyze the algorithm, and evaluate it empirically on synthetic and open-source NLP datasets.