  Recent advances in contextual bandit optimization and reinforcement learning
have garnered interest in applying these methods to real-world sequential
decision making problems. Real-world applications frequently have constraints
with respect to a currently deployed policy. Many of the existing
constraint-aware algorithms consider problems with a single objective (the
reward) and a constraint on the reward with respect to a baseline policy.
However, many important applications involve multiple competing objectives and
auxiliary constraints. In this paper, we propose a novel Thompson sampling
algorithm for multi-outcome contextual bandit problems with auxiliary
constraints. We empirically evaluate our algorithm on a synthetic problem.
Lastly, we apply our method to a real world video transcoding problem and
provide a practical way for navigating the trade-off between safety and
performance using Bayesian optimization.
