The conditional value at risk (CVaR) is a popular risk
measure which enables risk-averse decision making under uncertainty. We consider maximizing the CVaR of
a continuous submodular function, an extension of submodular set functions to a continuous domain. One example application is allocating a continuous amount of
energy to each sensor in a network, with the goal of
detecting intrusion or contamination. Previous work allows maximization of the CVaR of a linear or concave
function. Continuous submodularity represents a natural
set of nonconcave functions with diminishing returns,
to which existing techniques do not apply. We give a
(1 − 1/e)-approximation algorithm for maximizing the
CVaR of a monotone continuous submodular function.
This also yields an algorithm for submodular set functions which produces a distribution over feasible sets
with guaranteed CVaR. Experimental results in two sensor placement domains confirm that our algorithm substantially outperforms competitive baselines.