  User preference learning is generally a hard problem. Individual preferences
are typically unknown even to users themselves, while the space of choices is
infinite. Here we study user preference learning from information-theoretic
perspective. We model preference learning as a system with two interacting
sub-systems, one representing a user with his/her preferences and another one
representing an agent that has to learn these preferences. The user with
his/her behaviour is modeled by a parametric preference function. To
efficiently learn the preferences and reduce search space quickly, we propose
the agent that interacts with the user to collect the most informative data for
learning. The agent presents two proposals to the user for evaluation, and the
user rates them based on his/her preference function. We show that the optimum
agent strategy for data collection and preference learning is a result of
maximin optimization of the normalized weighted Kullback-Leibler (KL)
divergence between true and agent-assigned predictive user response
distributions. The resulting value of KL-divergence, which we also call
remaining system uncertainty (RSU), provides an efficient performance metric in
the absence of the ground truth. This metric characterises how well the agent
can predict user and, thus, the quality of the underlying learned user
(preference) model. Our proposed agent comprises sequential mechanisms for user
model inference and proposal generation. To infer the user model (preference
function), Bayesian approximate inference is used in the agent. The data
collection strategy is to generate proposals, responses to which help resolving
uncertainty associated with prediction of the user responses the most. The
efficiency of our approach is validated by numerical simulations. Also a
real-life example of preference learning application is provided.
