  Even when unable to run experiments, practitioners can evaluate prospective
policies, using previously logged data. However, while the bandits literature
has adopted a diverse set of objectives, most research on off-policy evaluation
to date focuses on the expected reward. In this paper, we introduce Lipschitz
risk functionals, a broad class of objectives that subsumes conditional
value-at-risk (CVaR), variance, mean-variance, many distorted risks, and CPT
risks, among others. We propose Off-Policy Risk Assessment (OPRA), a framework
that first estimates a target policy's CDF and then generates plugin estimates
for any collection of Lipschitz risks, providing finite sample guarantees that
hold simultaneously over the entire class. We instantiate OPRA with both
importance sampling and doubly robust estimators. Our primary theoretical
contributions are (i) the first uniform concentration inequalities for both CDF
estimators in contextual bandits and (ii) error bounds on our Lipschitz risk
estimates, which all converge at a rate of $O(1/\sqrt{n})$.
