Interactive preference elicitation under noisy preference models: An efficient non-Bayesian approach

The development of models that can cope with noisy input preferences is a critical topic in artificial intelligence methods for interactive preference elicitation. A Bayesian representation of the uncertainty in the user preference model can be used to successfully handle this, but there are large costs in terms of the processing time which limit the adoption of these techniques in real-time contexts. A Bayesian approach also requires one to assume a prior distribution over the set of user preference models. In this work, dealing with multi-criteria decision problems, we consider instead a more qualitative approach to preference uncertainty, focusing on the most plausible user preference models, and aim to generate a query strategy that enables us to find an alternative that is optimal in all of the most plausible preference models. We develop a non-Bayesian algorithmic method for recommendation and interactive elicitation that considers a large number of possible user models that are evaluated with respect to their degree of consistency of the input preferences. This suggests methods for generating queries that are reasonably fast to compute. We show formal asymptotic results for our algorithm, including the probability that it returns the actual best option. Our test results demonstrate the viability of our approach, including in real-time contexts, with high accuracy in recommending the most preferred alternative for the user.