论文标题
在潜在沉重的尾巴下以基于CVAR的反馈来学习
Learning with CVaR-based feedback under potentially heavy tails
论文作者
论文摘要
我们研究的学习算法试图最大程度地减少有条件的危险价值（CVAR），而所有学习者都知道，所产生的损失可能会被重尾。首先，我们研究了一个可能重尾随机变量的CVAR的通用估计器，这在实践中易于实现，只需要有限的方差和分布函数，而分布函数并不会仅仅在关注的分数周围变化太快或放慢速度。借助此估计量，我们得出了一种新的学习算法，该算法在随机梯度驱动的子过程中生产的候选者中可靠地选择。在此过程中，我们提供了高概率过多的CVAR界限，并补充了我们对基础CVAR估计量和从中得出的学习算法进行经验测试的理论。
We study learning algorithms that seek to minimize the conditional value-at-risk (CVaR), when all the learner knows is that the losses incurred may be heavy-tailed. We begin by studying a general-purpose estimator of CVaR for potentially heavy-tailed random variables, which is easy to implement in practice, and requires nothing more than finite variance and a distribution function that does not change too fast or slow around just the quantile of interest. With this estimator in hand, we then derive a new learning algorithm which robustly chooses among candidates produced by stochastic gradient-driven sub-processes. For this procedure we provide high-probability excess CVaR bounds, and to complement the theory we conduct empirical tests of the underlying CVaR estimator and the learning algorithm derived from it.
