Bayesian Optimization of Risk Measures

• URL: http://arxiv.org/abs/2007.05554v3
• Date: Wed, 4 Nov 2020 01:17:35 GMT
• Title: Bayesian Optimization of Risk Measures
• Authors: Sait Cakmak, Raul Astudillo, Peter Frazier and Enlu Zhou
• Abstract summary: We consider Bayesian optimization of objective functions of the form $rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function. We propose a family of novel Bayesian optimization algorithms that exploit the structure of the objective function to substantially improve sampling efficiency.
• Score: 7.799648230758491
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider Bayesian optimization of objective functions of the form $\rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $\rho$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness induced by the environmental random variable $W$. Such problems arise in decision making under uncertainty, such as in portfolio optimization and robust systems design. We propose a family of novel Bayesian optimization algorithms that exploit the structure of the objective function to substantially improve sampling efficiency. Instead of modeling the objective function directly as is typical in Bayesian optimization, these algorithms model $F$ as a Gaussian process, and use the implied posterior on the objective function to decide which points to evaluate. We demonstrate the effectiveness of our approach in a variety of numerical experiments.

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