UTA-poly and UTA-splines: additive value functions with polynomial marginals

TL;DR

This paper introduces a novel approach for inferring polynomial and spline marginal value functions in additive utility models using semidefinite programming, improving the flexibility and accuracy of decision analysis.

Contribution

It proposes replacing piecewise linear marginals with polynomial and spline functions via semidefinite programming, enhancing model expressiveness in additive utility functions.

Findings

Semidefinite programming effectively infers polynomial and spline marginals.

The new method improves the flexibility of utility function modeling.

Experimental results demonstrate the approach's viability.

Abstract

Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the alternative on the different criteria of the decision problem. The score of an alternative is determined by a marginal value function that evolves monotonically as a function of the performance of the alternative on this criterion. Determining the shape of the marginals is not easy for a decision maker. It is easier for him/her to make statements such as "alternative $a$ is preferred to $b$". In order to help the decision maker, UTA disaggregation procedures use linear programming to approximate the marginals by piecewise linear functions based only on such statements. In this paper, we propose to infer polynomials and splines instead of piecewise linear functions for the marginals. In this aim, we use semidefinite programming instead of linear programming. We illustrate this new elicitation method and present some experimental results.