Data-driven estimation in equilibrium using inverse optimization
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10107_2014_819_ReferencePDF.pdf
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Author(s)
Gupta, Vishal
Paschalidis, Ioannis Ch.
Bertsimas, Dimitris J
Date Issued
September 2014
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Bertsimas, Dimitris, Vishal Gupta, and Ioannis Ch. Paschalidis. "Data-driven estimation in equilibrium using inverse optimization." Mathematical Programming 153:2 (November 2015), pp 595-633.
Version
Author's final manuscript
Abstract
Equilibrium modeling is common in a variety of fields such as game theory and transportation science. The inputs for these models, however, are often difficult to estimate, while their outputs, i.e., the equilibria they are meant to describe, are often directly observable. By combining ideas from inverse optimization with the theory of variational inequalities, we develop an efficient, data-driven technique for estimating the parameters of these models from observed equilibria. We use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data. A distinguishing feature of our approach is that it supports both parametric and nonparametric estimation by leveraging ideas from statistical learning (kernel methods and regularization operators). In computational experiments involving Nash and Wardrop equilibria in a nonparametric setting, we find that a) we effectively estimate the unknown demand or congestion function, respectively, and b) our proposed regularization technique substantially improves the out-of-sample performance of our estimators.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10107-014-0819-4
