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.
翻译:价值风险(VaR)是评估具有随机环境因素的重大现实应用的风险的既定措施,本文件介绍了一种新的VaR最高置信度(V-UCB)算法,目的是尽可能扩大黑箱目标功能的VaR值,首先提供无风险保证。为了实现这一点,我们首先获得VaR的置信度,然后证明环境随机变量的值的存在(选择该变量是为了不后悔),这样VaR的置信度就属于按这种值评估的客观功能的内涵。我们的V-UCB算法从经验上展示了优化合成基准功能、组合优化问题和模拟机器人任务方面的最先进的性能。