  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.
