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arXiv · 2006.02001

Learning with CVaR-based feedback under potentially heavy tails

Matthew J. Holland·El Mehdi Haress
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Abstract

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.

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Matthew J. Holland, El Mehdi Haress. 2020-06-03. Learning with CVaR-based feedback under potentially heavy tails. https://arxiv.org/abs/2006.02001

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