Value-at-Risk Optimization with Gaussian Processes
This addresses risk assessment in critical real-world applications like finance and robotics, offering a new algorithmic approach with theoretical guarantees.
The paper tackles the problem of optimizing Value-at-Risk (VaR) for black-box functions with random environmental factors, introducing a novel V-UCB algorithm that achieves the first no-regret guarantee and demonstrates state-of-the-art performance in synthetic benchmarks, portfolio optimization, and a simulated robot task.
Value-at-risk (VaR) is an established measure to assess risks in critical real-world applications with random environmental factors. This paper presents a novel VaR upper confidence bound (V-UCB) algorithm for maximizing the VaR of a black-box objective function with the first no-regret guarantee. To realize this, we first derive a confidence bound of VaR and then prove the existence of values of the environmental random variable (to be selected to achieve no regret) such that the confidence bound of VaR lies within that of the objective function evaluated at such values. Our V-UCB algorithm empirically demonstrates state-of-the-art performance in optimizing synthetic benchmark functions, a portfolio optimization problem, and a simulated robot task.