论文标题
Pac-Bayesian限制有条件价值处于风险
PAC-Bayesian Bound for the Conditional Value at Risk
论文作者
论文摘要
有条件价值处于风险（CVAR）是“连贯的风险度量”一家，它推广了传统的数学期望。它在数学金融中广泛使用，它使人们对机器学习的兴趣越来越大，例如作为正则化的另一种方法，并作为确保公平性的一种手段。本文提出了一种用于学习算法的概括，以最大程度地减少经验损失的CVAR。绑定是Pac-bayesian类型的，当经验CVAR很小时，保证会很小。我们通过将CVAR估算到仅估计预期的问题来实现这一目标。然后，这使我们作为一种副产品，即使无限的随机变量是无限的，即使是副产品，也能够获得CVAR的浓度不平等。
Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an alternate approach to regularization, and as a means for ensuring fairness. This paper presents a generalization bound for learning algorithms that minimize the CVaR of the empirical loss. The bound is of PAC-Bayesian type and is guaranteed to be small when the empirical CVaR is small. We achieve this by reducing the problem of estimating CVaR to that of merely estimating an expectation. This then enables us, as a by-product, to obtain concentration inequalities for CVaR even when the random variable in question is unbounded.
