Cautious Learning of Multiattribute Preferences

TL;DR

This paper introduces a cautious learning approach for multi-attribute preference prediction that emphasizes reliability by only making predictions when all simple models agree, ensuring compatibility with any strict weak order.

Contribution

It proposes a novel cautious learning framework that guarantees model generality and prediction reliability by considering all simple models consistent with training data.

Findings

Predictions are reliable when all simple models agree.

The approach effectively balances prediction coverage and reliability.

Numerical tests demonstrate the method's robustness and applicability.

Abstract

This paper is dedicated to a cautious learning methodology for predicting preferences between alternatives characterized by binary attributes (formally, each alternative is seen as a subset of attributes). By "cautious", we mean that the model learned to represent the multi-attribute preferences is general enough to be compatible with any strict weak order on the alternatives, and that we allow ourselves not to predict some preferences if the data collected are not compatible with a reliable prediction. A predicted preference will be considered reliable if all the simplest models (following Occam's razor principle) explaining the training data agree on it. Predictions are based on an ordinal dominance relation between alternatives [Fishburn and LaValle, 1996]. The dominance relation relies on an uncertainty set encompassing the possible values of the parameters of the multi-attribute utility function. Numerical tests are provided to evaluate the richness and the reliability of the predictions made.