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Learning with risk-averse feedback under potentially heavy tails

Matthew Holland · El Mehdi Haress

Keywords: [ Learning Theory and Statistics ] [ Statistical Learning Theory ]


We study learning algorithms that seek to minimize the conditional value-at-risk (CVaR), when all the learner knows is that the losses (and gradients) 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, obtain excess CVaR bounds, and finally complement the theory with a regression application.

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