Bayesian Active Learning for Choice Models with Deep Gaussian Processes

This paper proposes an active learning algorithm and models which can gradually learn individual's preference through pairwise comparisons. The active learning scheme aims at finding individual's most preferred choice (e.g. an airline itinerary) with minimized number of pairwise comparisons. The pairwise comparisons are encoded into probabilistic models based on assumptions of choice models and deep Gaussian processes. More specifically, this paper develops two novel probabilistic models assuming correlated Gumbel noises and latent utility functions. One is based on shallow Gaussian priors and the other assumes deep Gaussian priors. In the active learning algorithm, the next-to-compare decision is determined by an original acquisition function. The proposed algorithm and models have been benchmarked using functions with multiple local optima and one public airline itinerary dataset. In both experiments, nests are designed to capture correlated Gumbel noises. The experiments indicate the effectiveness of our active learning algorithm and models. The deep Gaussian models are proven to find the best choice with a lower number of pairwise comparisons than the shallow one. In both experiments, deep Gaussian models outperform the shallow model. The shallow model is recommended when the choice set is large and less computational time is required (e.g. in one experiment, deep Gaussian models require approximately 60%-70% more time on average).