Learning with CVaR-based feedback under potentially heavy tails
This work addresses robust risk-sensitive learning for applications where data may have heavy tails, offering a practical solution with theoretical guarantees, though it appears incremental as it builds on existing CVaR and stochastic gradient methods.
The authors tackled the problem of learning algorithms that minimize conditional value-at-risk (CVaR) under potentially heavy-tailed losses, developing a general-purpose CVaR estimator and a new robust learning algorithm. They provided high-probability excess CVaR bounds and conducted empirical tests to validate their approach.
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.