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Stochastic Optimization in a Cumulative Prospect Theory Framework
Date Issued
01-09-2018
Author(s)
Jie, Cheng
Indian Institute of Technology, Madras
Fu, Michael
Marcus, Steve
Szepesvári, Csaba
Abstract
Cumulative prospect theory (CPT) is a popular approach for modeling human preferences. It is based on probabilistic distortions and generalizes the expected utility theory. We bring the CPT to a stochastic optimization framework and propose algorithms for both estimation and optimization of CPT-value objectives. We propose an empirical distribution function-based scheme to estimate the CPT value, and then, use this scheme in the inner loop of a CPT-value optimization procedure. We propose both gradient based as well as gradient-free CPT-value optimization algorithms that are based on two well-known simulation optimization ideas: simultaneous perturbation stochastic approximation and model-based parameter search, respectively. We provide theoretical convergence guarantees for all the proposed algorithms and also illustrate the potential of CPT-based criteria in a traffic signal control application.
Volume
63