  Contextual bandits with average-case statistical guarantees are inadequate in
risk-averse situations because they might trade off degraded worst-case
behaviour for better average performance. Designing a risk-averse contextual
bandit is challenging because exploration is necessary but risk-aversion is
sensitive to the entire distribution of rewards; nonetheless we exhibit the
first risk-averse contextual bandit algorithm with an online regret guarantee.
We conduct experiments from diverse scenarios where worst-case outcomes should
be avoided, from dynamic pricing, inventory management, and self-tuning
software; including a production exascale data processing system.
