A Mathematical Programming-Based Approach to Determining Objective Functions from Qualitative and Subjective Comparisons

Authors

  • Takayuki Yoshizumi IBM Research - Tokyo

DOI:

https://doi.org/10.1609/aaai.v29i1.9567

Keywords:

machine learning, mathematical programming

Abstract

The solutions or states of optimization problems or simulations are evaluated by using objective functions. The weights for these objective functions usually have to be estimated from experts' evaluations, which are likely to be qualitative and somewhat subjective. Although such estimation tasks are normally regarded as quite suitable for machine learning, we propose a mathematical programming-based method for better estimation. The key idea of our method is to use an ordinal scale for measuring paired differences of the objective values as well as the paired objective values. By using an ordinal scale, experts' qualitative and subjective evaluations can be appropriately expressed with simultaneous linear inequalities, and which can be handled by a mathematical programming solver. This allows us to extract more information from experts' evaluations compared to machine-learning-based algorithms, which increases the accuracy of our estimation. We show that our method outperforms machine-learning-based algorithms in a test of finding appropriate weights for an objective function.

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Published

2015-02-21

How to Cite

Yoshizumi, T. (2015). A Mathematical Programming-Based Approach to Determining Objective Functions from Qualitative and Subjective Comparisons. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1). https://doi.org/10.1609/aaai.v29i1.9567

Issue

Section

Main Track: Novel Machine Learning Algorithms