Bayesian Optimization of Risk Measures
This addresses decision-making under uncertainty in domains like portfolio optimization and robust systems design, representing an incremental improvement by adapting existing Bayesian optimization methods to risk measure contexts.
The paper tackles the problem of optimizing risk measures like VaR or CVaR in expensive black-box functions, proposing Bayesian optimization algorithms that model the underlying function as a Gaussian process to improve sampling efficiency, with effectiveness demonstrated in numerical experiments.
We consider Bayesian optimization of objective functions of the form $ρ[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $ρ$ 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.