  In this work, we study the problem of user preference learning on the example
of parameter setting for a hearing aid (HA). We propose to use an agent that
interacts with a HA user, in order to collect the most informative data, and
learns user preferences for HA parameter settings, based on these data. We
model the HA system as two interacting sub-systems, one representing a user
with his/her preferences and another one representing an agent. In this system,
the user responses to HA settings, proposed by the agent. In our user model,
the responses are driven by a parametric user preference function. The agent
comprises the sequential mechanisms for user model inference and HA parameter
proposal generation. To infer the user model (preference function), Bayesian
approximate inference is used in the agent. Here we propose the normalized
weighted Kullback-Leibler (KL) divergence between true and agent-assigned
predictive user response distributions as a metric to assess the quality of
learned preferences. Moreover, our agent strategy for generating HA parameter
proposals is to generate HA settings, responses to which help resolving
uncertainty associated with prediction of the user responses the most. The
resulting data, consequently, allows for efficient user model learning. The
normalized weighted KL-divergence plays an important role here as well, since
it characterizes the informativeness of the data to be used for probing the
user. The efficiency of our approach is validated by numerical simulations.
