Learning Linear Utility Functions From Pairwise Comparison Queries
This work addresses the challenge of preference modeling for applications like recommendation systems, but it is incremental as it builds on existing utility learning frameworks.
The paper tackles the problem of learning linear utility functions from pairwise comparison queries, showing that in passive learning, predicting out-of-sample responses is efficiently learnable under certain conditions, while parameter recovery is not without strong assumptions. In active learning, both objectives become efficiently learnable, demonstrating a qualitative gap between the two settings.
We study learnability of linear utility functions from pairwise comparison queries. In particular, we consider two learning objectives. The first objective is to predict out-of-sample responses to pairwise comparisons, whereas the second is to approximately recover the true parameters of the utility function. We show that in the passive learning setting, linear utilities are efficiently learnable with respect to the first objective, both when query responses are uncorrupted by noise, and under Tsybakov noise when the distributions are sufficiently "nice". In contrast, we show that utility parameters are not learnable for a large set of data distributions without strong modeling assumptions, even when query responses are noise-free. Next, we proceed to analyze the learning problem in an active learning setting. In this case, we show that even the second objective is efficiently learnable, and present algorithms for both the noise-free and noisy query response settings. Our results thus exhibit a qualitative learnability gap between passive and active learning from pairwise preference queries, demonstrating the value of the ability to select pairwise queries for utility learning.